Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended topological quantum field theories, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for categorifying things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory. In particular, it should not be necessary to be familiar with any category theory, although it will of course help