The rewriting calculus embeds in a same setting the lambda calculus and the rewriting, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the lambda-calculus and the pattern matching facilities of the rewriting are then both available at the same level. It is worth noticing that the complexity of the calculu breaks the confluence property, so that we need to define appropiate strategies or restrictions, in order to recover it. We choose here to look at the rho-calculus as an extension of the lambda-calculus, and we study the typed aspects. Our study is based upon a generalization of Barendregt's lambda-cube, in which we unify both abstractors lambda and Pi into a single one. We need to deal with the original features of the rho-calculus too: matching power, non-determinism, confluence issues. With proper restrictions, we have proved most of the usual properties for typed calculi: substitution lemma, correctness of types, subject reduction, consistency. Uniqueness of typing is generally no longer valid but we can still prove it for one of the most restrictive systems, rho-> and rho2.