  We review recent advances in the numerical analysis of the Monge-Amp\`ere
equation. Various computational techniques are discussed including wide-stencil
finite difference schemes, two-scaled methods, finite element methods, and
methods based on geometric considerations. Particular focus is the development
of appropriate stability and consistency estimates which lead to rates of
convergence of the discrete approximations. Finally we present numerical
experiments which highlight each method for a variety of test problem with
different levels of regularity.
