  VB-groupoids are vector bundles in the category of Lie groupoids. They
encompass several classical objects, including Lie group representations and
2-vector spaces. Moreover, they provide geometric pictures for 2-term
representations up to homotopy of Lie groupoids. We attach to every VB-groupoid
a cochain complex controlling its deformations and discuss its fundamental
features, such as Morita invariance and a van Est theorem. Several examples and
applications are given.
