The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and velocity-strengthening behaviors. Slowly extending, loading-rate-dependent creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions, and velocity-strengthening friction. Nonlinear propagating rupture fronts-the outcome of instability-depend sensitively on the stress state and velocity-strengthening friction. Rupture fronts span a wide range of propagation velocities and are related to steady-state-front solutions.