We present a simple theoretical model for adsorption of colloidal particles onto vesicles. The contact energy of adhesion is balanced by the tension and curvature energies of the vesicle membrane under the constraint of fixed volume, with the geometry of the complex determined by a variational calculation. Physical observables, such as the degree of penetration or the membrane tension, are investigated as functions of colloidal size and adhesion, tension, and bending energies. We find various new (and discontinuous) transitions in the geometry of the complex compared to those from a description that neglects the curvature contribution. Particular emphasis is put on the transition from the partly to the fully wrapped state and on unbinding of the complex at weak adhesion energy or small colloidal size. The above model can be thought of as a phenomenological theory of the initial steps involved in biological endocytosis and aims toward an improved physical understanding of this process.