  This is a review of recent results on the integrable structure of the
ordinary and modified melting crystal models. When deformed by special external
potentials, the partition function of the ordinary melting crystal model is
known to become essentially a tau function of the 1D Toda hierarchy. In the
same sense, the modified model turns out to be related to the Ablowitz-Ladik
hierarchy. These facts are explained with the aid of a free fermion system,
fermionic expressions of the partition functions, algebraic relations among
fermion bilinears and vertex operators, and infinite matrix representations of
those operators.
