  We review quantum Monte Carlo methods for dealing with large shell model
problems. These methods reduce the imaginary-time many-body evolution operator
to a coherent superposition of one-body evolutions in fluctuating one-body
fields; the resultant path integral is evaluated stochastically. We first
discuss the motivation, formalism, and implementation of such Shell Model Monte
Carlo (SMMC) methods. There then follows a sampler of results and insights
obtained from a number of applications. These include the ground state and
thermal properties of {\it pf}-shell nuclei, the thermal and rotational
behavior of rare-earth and $\gamma$-soft nuclei, and the calculation of double
beta-decay matrix elements. Finally, prospects for further progress in such
calculations are discussed.
