After a brief review of accretive operators and the classical
theory of nonlinear semigroups, I will describe some recent work on nonlinear
semigroup methods for parabolic variational inequalities.  Applications of
these abstract results to concrete problems, such as free boundary problems
in Sobolev spaces and degenerate parabolic equations, will be given.
If time permits, I will discuss extensions of these results to evolution families for
nonautonomous operators and constraints.