  In this article, we review quantile models with endogeneity. We focus on
models that achieve identification through the use of instrumental variables
and discuss conditions under which partial and point identification are
obtained. We discuss key conditions, which include monotonicity and
full-rank-type conditions, in detail. In providing this review, we update the
identification results of Chernozhukov and Hansen (2005, Econometrica). We
illustrate the modeling assumptions through economically motivated examples. We
also briefly review the literature on estimation and inference.
  Key Words: identification, treatment effects, structural models, instrumental
variables
