In a real vector space addition is settled by scalar multiplication. This lead us to the following description of smooth vector bundles: they are manifolds endowed with a nice action of the multiplicative monoid of the real numbers. In this talk I will deal with vector bundles over Lie groupoids and algebroids. Lie groupoids are presentations for singular smooth spaces, constitute a concrete unified framework to deal with manifolds, Lie groups, actions, foliations and others. Lie algebroids are their infinitesimal counterpart, together they play a rich theory in actual development. Vector bundles over groupoids and algebroids are generalized representations and help us to understand the geometry of our singular spaces. I will present definitions and examples, provide a characterization by using the multiplicative monoid, and discuss the integration of these structures. This is part of a joint work with H. Bursztyn and A. Cabrera.