When a liquid droplet is placed on a flat smooth, and rigid solid, its spreading to equilibrium can be described by a dynamic energy balance. Excess free surface (interfacial) energy, resulting from the capillary imbalance, is dissipated by viscous motion within the liquid. If the solid is sufficiently soft, a local deformation, or "wetting ridge". may form near the wetting front, and its motion may lead to viscoelastic dissipation. We describe the case in which viscoelastic dissipation dominates and thus where spreading speed is controlled by bulk properties of the solid, rather than by liquid viscosity. A parallel is drawn with elastomeric adhesion.