Chapter 27 § 666 (Jurisdiction) of the Charter sets forth the Board's authority as follows:
1. To make, amend and repeal rules and regulations for carrying into effect the provisions of the laws, resolutions, rules and regulations in respect to any subject-matter jurisdiction whereof is conferred by law upon the board, and to include in such rules and regulations provisions applying to specific conditions and prescribing means and methods of practice to effectuate such provisions and for carrying into effect the powers of the board.
2. To make, amend and repeal rules and regulations for the enforcement of those provisions of the labor law and other laws which relate to the construction or alteration of, structural changes in plumbing and drainage of, elevators in, fire escapes on, adequacy and means of exit from, or fire protection in, all buildings within the city, which shall take the place of the industrial code and of any rules and regulations of the department of labor of the state of New York relating to the same subject-matter.
3. To make, amend and repeal rules, regulations and directives governing the preparation and presentation by the director of matters before the board.
4. To exercise exclusively with respect to buildings situated within the city, the same powers as are exercised by the department of labor of the state of New York elsewhere in the state.
5. To determine and vary the application of the zoning resolution as may be provided in such resolution and pursuant to section six hundred sixty-eight.
6. To hear and decide appeals from and review,
(a) except as otherwise provided by law, any order, requirement, decision or determination of the commissioner of buildings or of a deputy commissioner of buildings or any borough superintendent of buildings acting under a written delegation of power from the commissioner of buildings filed in accordance with the provisions of section six hundred forty-two or section six hundred forty-five of this charter, or
(b) any order, requirement, decision or determination of the fire commissioner or any rule or regulation or amendment or repeal thereof made by the fire commissioner, or
(c) any order, requirement, decision or determination of the commissioner of transportation or the commissioner of ports and trade made in relation to the structures or uses on water front property under his or her jurisdiction in connection with the application or enforcement of the provisions of the zoning resolution of the city of New York, the labor law and such other laws, rules and regulations as may govern the construction, alteration, maintenance, use, occupancy, safety, sanitary conditions, mechanical equipment and inspection of structures in the city, under the authority conferred upon them by law, by reversing or affirming in whole or in part, or modifying the order, regulation, decision or determination appealed from, and to make such order, requirement, decision or determination as in its opinion ought to be made in the premises, and to that end shall have the power of the officer from whose ruling the appeal is taken, and of any officer under whose written delegation of power such ruling was made.
7. In passing upon appeals, to vary or modify any rule or regulation or the provisions of any law relating to the construction, use, structural changes, equipment, alteration or removal of buildings or structures, or vaults in sidewalks appurtenant thereto, where there are practical difficulties or unnecessary hardship in the way of carrying out the strict letter of the law, so that the spirit of the law shall be observed, public safety secured and substantial justice done, provided that the provisions of the housing maintenance code and of any regulation or order issued under such code may be varied or modified only to the extent permitted by such code and only in the manner and subject to the conditions therein specified.
8. To review, upon motion of any member of the board, any rule, regulation, amendment or repeal thereof, and any order, requirement, decision or determination from which an appeal may be taken to the board under the provisions of this chapter or of any law, or of any rule, regulation or decision of the board; but no such review shall prejudice the rights of any person who has in good faith acted thereon before it is reversed or modified. The provisions of this chapter relating to appeals to the board shall be applicable to such review.
9. To afford an equal right to the city planning commission, community boards, and borough boards and lessees and tenants as well as owners to appear before it for the purpose of proposing arguments or submitting evidence in respect of any matter brought before it pursuant to the zoning resolution of the city of New York.
10. To issue such special permits as the board is authorized to issue under the zoning resolution.
11. To revoke or modify, upon due notice and hearing, variances and special permits previously granted under the zoning resolution if the terms and conditions of such grants have been violated.