Dirac’s theory of constrained Hamiltonian systems is first described, discussing in detail primary and secondary constraints, first-class and second-class constraints, Dirac brackets, effective Hamiltonian, total Hamiltonian and extended Hamiltonian. On quantization, the operator versions of first-class constraints become supplementary conditions on the wave function, provided these constraints are consistent with one another and with the Schrodinger equation. Second-class constraints, if they cannot be brought into the first class by independent linear combinations, become instead equations between operators in the quantum theory. Moreover, commutation relations are taken to correspond to Dirac-bracket relations, provided it is possible to find an irreducible representation of the Dirac-brackets algebra. Alternative approaches also exist, where second-class constraints are not eliminated at the classical level, and play instead a relevant role in the quantum theory.