  The aim of this report is to give an overview of the duality between type IIB
string theory on the maximally supersymmetric PP-wave and the BMN sector of N=4
Super Yang-Mills theory. The general features of the string and the field
theory descriptions are reviewed, but the main focus of this report is on the
comparison between the two sides of the duality. In particular, it is first
explained how free IIB strings emerge on the gauge theory side and then the
generalizations of this relation to the full interacting theory are considered.
An ``historical'' approach is taken and the various proposals presented in the
literature are described.
