VB-groupoids are vector bundles over Lie groupoids. They arise naturally, with the tangent and cotangent constructions as prominent examples, and admit a nice interpretation in terms of representations up to homotopy. In this talk I will review these concepts and describe the behavior of vector bundles under Morita equivalences. I will explain how this leads to a convenient notion of 2-vector bundle over stacks, present some applications to Poisson geometry, and discuss further lines of research. (Joint with C. Ortiz, arXiv:1612.09289)