This paper deals with the sensitivity analysis of solutions of variational inequalities by an implicit-function approach that makes use of so-called normal maps. Although some of the results can be extended to infinite-dimensional spaces, the treatment here is restricted to variational inequalities over polyhedral convex sets in finite-dimensional spaces, the case for which the strongest results can be established. Coverage includes transformation of the variational inequality to the equivalent form of a normal map, basic facts about normal maps, derivatives, conditions for nonsingularity, the implicit-function theorem, and applications to sensitivity analysis. Some examples are included to illustrate the techniques.