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.