I'll give a broad introduction to the representation theory of the exterior algebra Λg of a simple Lie algebra g. Then I will concentrate on the study of the space of covariants A = (Λg⊗g)^g (which describes the isotypic component of type g in Λg) as a module over the algebra of invariants (Λg)^g. I will also discuss generalizations of this result and some related problems. Joint project with C. De Concini and C. Procesi (and partly with P. Moseneder Frajria).