  We review the construction of exactly solvable lattice models whose continuum
limits are $N=2$ supersymmetric models. Both critical and off-critical models
are discussed. The approach we take is to first find lattice models with
natural topological sectors, and then identify the continuum limits of these
sectors with topologically twisted $N=2$ supersymmetric field theories. From
this, we then describe how to recover the complete lattice versions of the
$N=2$ supersymmetric field theories. We discuss a number of simple physical
examples and we describe how to construct a broad class of models. We also give
a brief review of the scattering matrices for the excitations of these models.
(Contribution to the procedings of the Cargese meeting on ``String Theory,
Conformal Models and Topological Field Theories'', May 12-21, 1993.)
