the riemann mapping theorem (rmt) is a staple in complex analysis in one variable: {\it any simply connected domain in the plane (other than the plane itself) is biholomorphically equivalent to the unit disk.} a direct analog is not true in two dimensions and higher. as discovered by poincar\'e, the unit ball in $c^2$ is not biholomorphic to the bidisk. the reason is that in higher dimensions the boundary of a domain inherits a non-trivial structure---a cr structure--- from the ambient complex structure. we will discuss how one can formulate a version of the rtm that holds in higher dimensions as well. after this introduction, we shall mention some current fundamental problem in this area.