Theoretical presentations of the rho-calculus often treat the matching constraint computations as an atomic operation although matching constraints are explicitly expressed. Actual implementations have to take a much more realistic view: computations needed in order to find the solutions of a matching equation can have an important impact on the (efficiency of the) calculus for some matching theories and the substitution application usually involves a term traversal. Following the works on explicit substitutions in the -calculus, we present two versions of the rho-calculus, one with explicit matching and one with explicit substitutions, together with a version that combines the two and considers efficiency issues and more precisely the composition of substitutions. The approach is general, allowing the extension to various matching theories. We establish the confluence of the calculus and the termination of the explicit constraint handling and application sub-calculus.