We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. More specifically, we exploit the equivalence between intrinsic reparameterization and extrinsic tangential velocity to reduce the gradient flow near (quasi-)steady states to a tractable dynamical system defined on a stationary domain. These theoretical results are applied to derive and study dynamics of pattern forming systems such as faceted interfaces and self-adhesion membranes.