We survey some important results concerning the finite--dimensional
representations of the loop algebra of a simple complex Lie algebra, and their
twisted loop subalgebras. In particular, we review the parametrization and
description of the Weyl modules and of the irreducible finite--dimensional
representations of such algebras, describe a block decomposition of the
(non--semisimple) category of their finite--dimensional representations, and
conclude with recent developments in the representation theory of multiloop
algebras.