  Since its introduction over 50 years ago, the concept of Mosco convergence
has permeated through diverse areas of mathematics and applied sciences. These
include applied analysis, the theory of partial differential equations,
numerical analysis, and infinite dimensional constrained optimization, among
others. In this paper we explore some of the consequences of Mosco convergence
on applied problems that involve moving sets, with some historical accounts,
and modern trends and features. In particular, we focus on connections with
density of convex intersections, finite element approximations,
quasi-variational inequalities, and impulse problems.
