In broad terms, classification in mathematics means finding a clear and useful way to describe the isomorphism classes of a given category, such as those of finite simple groups or division algebras. In the case of C*-algebras and groupoids, the main goal is to classify objects up to Morita equivalence. Morita equivalence can be described by the existence of a pair of mutually inverse imprimitivity bimodules. This suggests that the right setting is the category whose objects are C*-algebras and whose arrows are isomorphism classes of Hilbert bimodules. However, once we identify bimodules up to isomorphism, the resulting category becomes non-concrete and difficult to handle. A better approach is to include bimodule homomorphisms as a second layer of arrows, which gives a bicategory (a weak 2-category). Many well-known C*-algebraic constructions, such as Cuntz?Pimsner algebras, can then be described by universal properties in this bicategory. I will explain how this framework leads to a gauge-equivariant homotopy classification of graph C*-algebras of finite regular graphs. The talk is based on joint work with Adam Dor-On and Efren Ruiz.