  The shell model Monte Carlo (SMMC) method enables calculations in model
spaces that are many orders of magnitude larger than those that can be treated
by conventional methods, and is particularly suitable for the calculation of
level densities in the presence of correlations. We review recent advances and
applications of SMMC for the microscopic calculation of level densities. Recent
developments include (i) a method to calculate accurately the ground-state
energy of an odd-mass nucleus, circumventing a sign problem that originates in
the projection on an odd number of particles, and (ii) a method to calculate
directly level densities, which, unlike state densities, do not include the
spin degeneracy of the levels. We calculated the level densities of a family of
nickel isotopes $^{59-64}$Ni and of a heavy deformed rare-earth nucleus
$^{162}$Dy and found them to be in close agreement with various experimental
data sets.
