The shell-model Monte Carlo (SMMC) or the auxiliary-field Monte Carlo (AFMC) method (as it is known in the greater community of many-body physics) stands out as a powerful computational technique in nuclear structure physics. It was developed in the framework of the interacting nuclear shell model as an alternative to direct diagonalization of the shell model Hamiltonian. Using theSMMC approach, one can carry out realistic calculations in much larger configuration spaces than those possible by conventional methods. This approachallows calculation of ground state, thermal and rotational properties of atomic nuclei and is particularly suitable for calculating nuclear properties at finite temperatures and excitation energies, thereby presenting significant applications for nuclear astrophysics. A general overview of the method and various nuclear applications with an emphasis on recent advances for the study of heavy nuclei with proton-neutron imbalance and large deformations will be presented. Applications of the method to other many-body problems will be exemplified for ultracold atomic gases.