Cell adhesion and motility depend strongly on the interactions between cells and extracellular matrix (ECM) substrates. When plated onto artificial adhesive surfaces, cells first flatten and deform extensively as they spread. At the molecular level, the interaction of membrane-based integrins with the ECM has been shown to initiate a complex cascade of signaling events , which subsequently triggers cellular morphological changes and results in the generation of contractile forces . Here, we focus on the early stages of cell spreading and probe their dynamics by quantitative visualization and biochemical manipulation with a variety of cell types and adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. We find that the dynamics of adhesion follows a universal power-law behavior. This is in sharp contrast with the common belief that spreading is regulated by either the diffusion of adhesion receptors toward the growing adhesive patch [3-5] or by actin polymerization [6-8]. To explain this, we propose a simple quantitative and predictive theory that models cells as viscous adhesive cortical shells enclosing a less viscous interior. Thus, although cell spreading is driven by well-identified biomolecular interactions, it is dynamically limited by its mesoscopic structure and material properties.