Abstract: Tensor products and C*-norms play a prominent role in the theory of C*-algebras, in particular in the study of nuclear C*-algebras and semidiscrete (or injective) von Neumann algebras. This chapter extends part of that theory to nonselfadjoint operator algebras, and gives some applications. Topics covered include maximal and normal tensor products, joint dilations and the disc algebra, tenser products with triangular algebras, Pisier's delta norm, factorization through matrix spaces, and nuclearity and semidiscreteness for linear operators. Notes and historical remarks are presented at the end of the chapter.

Keywords: C*-norms, C*-algebras, nonselfadjoint operator algebras, joint dilations, disc algebra, triangular algebras, semidiscrete,