We review the characteristics and differences of the adhesion of living cells to surfaces compared to the adhesion of inert matter. In particular, we show that while mimicking cell adhesion by vesicles sheds light on the role of membrane fluctuations and ligand phase separation, it neglects the role of active processes that in live cells control the number of adhesion proteins and their spatial organization. Recent models that incorporate active cell contractility are shown to predict some of the features. In this review, we mainly focus on thermodynamic modeling approaches and outline challenges for future theoretical work. (C) Koninklijke Brill NV, Leiden, 2010