  This survey article on bivariant Kasparov theory and E-theory is mainly
intended for readers with a background in homotopical algebra and category
theory. We approach both bivariant K-theories via their universal properties
and equip them with extra structure such as a tensor product and a triangulated
category structure. We discuss the construction of the Baum-Connes assembly map
via localisation of categories and explain how this is related to the purely
topological construction by Davis and Lueck.
