Article 10: Right to public hearing

Everyone is entitled in full equality to a fair and public hearing by an independent and impartial tribunal, in the determination of his rights and obligations and of any criminal charge against him.

Definitions of the right to public hearings

The right to public hearings (as part of the right to a fair trial) is enshrined in 
Article 10 of the Universal Declaration of Human Rights.

The right is enshrined in Article 14 of the International Covenant on Civil and Political Rights:

1. All persons shall be equal before the courts and tribunals. In the determination of any criminal charge against him, or of his rights and obligations in a suit at law, everyone shall be entitled to a fair and public hearing by a competent, independent and impartial tribunal established by law. The press and the public may be excluded from all or part of a trial for reasons of morals, public order (ordre public) or national security in a democratic society, or when the interest of the private lives of the parties so requires, or to the extent strictly necessary in the opinion of the court in special circumstances where publicity would prejudice the interests of justice; but any judgement rendered in a criminal case or in a suit at law shall be made public except where the interest of juvenile persons otherwise requires or the proceedings concern matrimonial disputes or the guardianship of children.
2. Everyone charged with a criminal offence shall have the right to be presumed innocent until proved guilty according to law.
3. In the determination of any criminal charge against him, everyone shall be entitled to the following minimum guarantees, in full equality: 
(a) To be informed promptly and in detail in a language which he understands of the nature and cause of the charge against him;
(b) To have adequate time and facilities for the preparation of his defence and to communicate with counsel of his own choosing;
(c) To be tried without undue delay;
(d) To be tried in his presence, and to defend himself in person or through legal assistance of his own choosing; to be informed, if he does not have legal assistance, of this right; and to have legal assistance assigned to him, in any case where the interests of justice so require, and without payment by him in any such case if he does not have sufficient means to pay for it;
(e) To examine, or have examined, the witnesses against him and to obtain the attendance and examination of witnesses on his behalf under the same conditions as witnesses against him;
(f) To have the free assistance of an interpreter if he cannot understand or speak the language used in court;
(g) Not to be compelled to testify against himself or to confess guilt.
4. In the case of juvenile persons, the procedure shall be such as will take account of their age and the desirability of promoting their rehabilitation.
5. Everyone convicted of a crime shall have the right to his conviction and sentence being reviewed by a higher tribunal according to law.
6. When a person has by a final decision been convicted of a criminal offence and when subsequently his conviction has been reversed or he has been pardoned on the ground that a new or newly discovered fact shows conclusively that there has been a miscarriage of justice, the person who has suffered punishment as a result of such conviction shall be compensated according to law, unless it is proved that the non-disclosure of the unknown fact in time is wholly or partly attributable to him.
7. No one shall be liable to be tried or punished again for an offence for which he has already been finally convicted or acquitted in accordance with the law and penal procedure of each country.

In its General Comments No 13 of 1984, the Human Rights Committee comments on the administration of justice: http://www2.ohchr.org/english/bodies/hrc/comments.htm.

It is contained in Articles 12, 37 and 40 in the Convention on the Rights of the Child:

Article 12
1. States Parties shall assure to the child who is capable of forming his or her own views the right to express those views freely in all matters affecting the child, the views of the child being given due weight in accordance with the age and maturity of the child.
2. For this purpose, the child shall in particular be provided the opportunity to be heard in any judicial and administrative proceedings affecting the child, either directly, or through a representative or an appropriate body, in a manner consistent with the procedural rules of national law.

Article 37
States Parties shall ensure that:
(a) No child shall be subjected to torture or other cruel, inhuman or degrading treatment or punishment. Neither capital punishment nor life imprisonment without possibility of release shall be imposed for offences committed by persons below eighteen years of age;
(b) No child shall be deprived of his or her liberty unlawfully or arbitrarily. The arrest, detention or imprisonment of a child shall be in conformity with the law and shall be used only as a measure of last resort and for the shortest appropriate period of time;
(c) Every child deprived of liberty shall be treated with humanity and respect for the inherent dignity of the human person, and in a manner which takes into account the needs of persons of his or her age. In particular, every child deprived of liberty shall be separated from adults unless it is considered in the child's best interest not to do so and shall have the right to maintain contact with his or her family through correspondence and visits, save in exceptional circumstances;
(d) Every child deprived of his or her liberty shall have the right to prompt access to legal and other appropriate assistance, as well as the right to challenge the legality of the deprivation of his or her liberty before a court or other competent, independent and impartial authority, and to a prompt decision on any such action.

Article 40
1. States Parties recognize the right of every child alleged as, accused of, or recognized as having infringed the penal law to be treated in a manner consistent with the promotion of the child's sense of dignity and worth, which reinforces the child's respect for the human rights and fundamental freedoms of others and which takes into account the child's age and the desirability of promoting the child's reintegration and the child's assuming a constructive role in society.
2. To this end, and having regard to the relevant provisions of international instruments, States Parties shall, in particular, ensure that:
(a) No child shall be alleged as, be accused of, or recognized as having infringed the penal law by reason of acts or omissions that were not prohibited by national or international law at the time they were committed;
(b) Every child alleged as or accused of having infringed the penal law has at least the following guarantees:
(i) To be presumed innocent until proven guilty according to law;
(ii) To be informed promptly and directly of the charges against him or her, and, if appropriate, through his or her parents or legal guardians, and to have legal or other appropriate assistance in the preparation and presentation of his or her defence;
(iii) To have the matter determined without delay by a competent, independent and impartial authority or judicial body in a fair hearing according to law, in the presence of legal or other appropriate assistance and, unless it is considered not to be in the best interest of the child, in particular, taking into account his or her age or situation, his or her parents or legal guardians;
(iv) Not to be compelled to give testimony or to confess guilt; to examine or have examined adverse witnesses and to obtain the participation and examination of witnesses on his or her behalf under conditions of equality;
(v) If considered to have infringed the penal law, to have this decision and any measures imposed in consequence thereof reviewed by a higher competent, independent and impartial authority or judicial body according to law;
(vi) To have the free assistance of an interpreter if the child cannot understand or speak the language used;
(vii) To have his or her privacy fully respected at all stages of the proceedings.
3. States Parties shall seek to promote the establishment of laws, procedures, authorities and institutions specifically applicable to children alleged as, accused of, or recognized as having infringed the penal law, and, in particular:
(a) The establishment of a minimum age below which children shall be presumed not to have the capacity to infringe the penal law;
(b) Whenever appropriate and desirable, measures for dealing with such children without resorting to judicial proceedings, providing that human rights and legal safeguards are fully respected.
4. A variety of dispositions, such as care, guidance and supervision orders; counselling; probation; foster care; education and vocational training programmes and other alternatives to institutional care shall be available to ensure that children are dealt with in a manner appropriate to their well-being and proportionate both to their circumstances and the offence. 

It is also contained in Articles 16, 18 and 83 of the International Convention on the Protection of the Rights of All Migrant Workers and Members of Their Families:

Article 16
1. Migrant workers and members of their families shall have the right to liberty and security of person.
2. Migrant workers and members of their families shall be entitled to effective protection by the State against violence, physical injury, threats and intimidation, whether by public officials or by private individuals, groups or institutions.
3. Any verification by law enforcement officials of the identity of migrant workers or members of their families shall be carried out in accordance with procedure established by law.
4. Migrant workers and members of their families shall not be subjected individually or collectively to arbitrary arrest or detention; they shall not be deprived o their liberty except on such grounds and in accordance with such procedures as are established by law.
5. Migrant workers and members of their families who are arrested shall be informed at the time of arrest as far as possible in a language they understand of the reasons for their arrest and they shall be promptly informed in a language they understand of any charges against them.
6. Migrant workers and members of their families who are arrested or detained on a criminal charge shall be brought promptly before a judge or other officer authorized by law to exercise judicial power and shall be entitled to trial within a reasonable time or to release. It shall not be the general rule that while awaiting trial they shall be detained in custody, but release may be subject to guarantees to appear for trial, at any other stage of the judicial proceedings and, should the occasion arise, for the execution of the judgement.
7. When a migrant worker or a member of his or her family is arrested or committed to prison or custody pending trial or is detained in any other manner:
(a) The consular or diplomatic authorities of his or her State of origin or of a State representing the interests of that State shall, if he or she so requests, be informed without delay of his or her arrest or detention and of the reasons therefor;
(b) The person concerned shall have the right to communicate with the said authorities. Any communication by the person concerned to the said authorities shall be forwarded without delay, and he or she shall also have the right to receive communications sent by the said authorities without delay;
(c) The person concerned shall be informed without delay of this right and of rights deriving from relevant treaties, if any, applicable between the States concerned, to correspond and to meet with representatives of the said authorities and to make arrangements with them for his or her legal representation.
8. Migrant workers and members of their families who are deprived of their liberty by arrest or detention shall be entitled to take proceedings before a court, in order that that court may decide without delay on the lawfulness of their detention and order their release if the detention is not lawful. When they attend such proceedings, they shall have the assistance, if necessary without cost to them, of an interpreter, if they cannot understand or speak the language used.
9. Migrant workers and members of their families who have been victims of unlawful arrest or detention shall have an enforceable right to compensation.

Article 18
1. Migrant workers and members of their families shall have the right to equality with nationals of the State concerned before the courts and tribunals. In the determination of any criminal charge against them or of their rights and obligations in a suit of law, they shall be entitled to a fair and public hearing by a competent, independent and impartial tribunal established by law.
2. Migrant workers and members of their families who are charged with a criminal offence shall have the right to be presumed innocent until proven guilty according to law.
3. In the determination of any criminal charge against them, migrant workers and members of their families shall be entitled to the following minimum guarantees:
(a) To be informed promptly and in detail in a language they understand of the nature and cause of the charge against them;
(b) To have adequate time and facilities for the preparation of their defence and to communicate with counsel of their own choosing;
(c) To be tried without undue delay;
(d) To be tried in their presence and to defend themselves in person or through legal assistance of their own choosing; to be informed, if they do not have legal assistance, of this right; and to have legal assistance assigned to them, in any case where the interests of justice so require and without payment by them in any such case if they do not have sufficient means to pay;
(e) To examine or have examined the witnesses against them and to obtain the attendance and examination of witnesses on their behalf under the same conditions as witnesses against them;
(f) To have the free assistance of an interpreter if they cannot understand or speak the language used in court;
(g) Not to be compelled to testify against themselves or to confess guilt.
4. In the case of juvenile persons, the procedure shall be such as will take account of their age and the desirability of promoting their rehabilitation.
5. Migrant workers and members of their families convicted of a crime shall have the right to their conviction and sentence being reviewed by a higher tribunal according to law.
6. When a migrant worker or a member of his or her family has, by a final decision, been convicted of a criminal offence and when subsequently his or her conviction has been reversed or he or she has been pardoned on the ground that a new or newly discovered fact shows conclusively that there has been a miscarriage of justice, the person who has suffered punishment as a result of such conviction shall be compensated according to law, unless it is proved that the non-disclosure of the unknown fact in time is wholly or partly attributable to that person.
7. No migrant worker or member of his or her family shall be liable to be tried or punished again for an offence for which he or she has already been finally convicted or acquitted in accordance with the law and penal procedure of the State concerned.

Article 83
Each State Party to the present Convention undertakes:
(a) To ensure that any person whose rights or freedoms as herein recognized are violated shall have an effective remedy, notwithstanding that the violation has been committed by persons acting in an official capacity;
(b) To ensure that any persons seeking such a remedy shall have his or her claim reviewed and decided by competent judicial, administrative or legislative authorities, or by any other competent authority provided for by the legal system of the State, and to develop the possibilities of judicial remedy;
(c) To ensure that the competent authorities shall enforce such remedies when granted.

The right is also contained in Article 7 of the African Charter on Human and Peoples' Rights:

1. Every individual shall have the right to have his cause heard. This comprises:
(a) the right to an appeal to competent national organs against acts of violating his fundamental rights as recognized and guaranteed by conventions, laws, regulations and customs in force;
(b) the right to be presumed innocent until proved guilty by a competent court or tribunal;
(c) the right to defence, including the right to be defended by counsel of his choice;
(d) the right to be tried within a reasonable time by an impartial court or tribunal.
2. No one may be condemned for an act or omission which did not constitute a legally punishable offence at the time it was committed. No penalty may be inflicted for an offence for which no provision was made at the time it was committed. Punishment is personal and can be imposed only on the offender.