  We study finite dimensional representations of current algebras, loop
algebras and their quantized versions. For the current algebra of a simple Lie
algebra of type {\tt ADE}, we show that Kirillov-Reshetikhin modules and Weyl
modules are in fact all Demazure modules. As a consequence one obtains an
elementary proof of the dimension formula for Weyl modules for the current and
the loop algebra. Further, we show that the crystals of the Weyl and the
Demazure module are the same up to some additional label zero arrows for the
Weyl module.
  For the current algebra $\Lgc$ of an arbitrary simple Lie algebra, the fusion
product of Demazure modules of the same level turns out to be again a Demazure
module. As an application we construct the $\Lgc$-module structure of the
Kac-Moody algebra $\Lhg$-module $V(\ell\Lam_0)$ as a semi-infinite fusion
product of finite dimensional $\Lgc$--modules.
