Compressed sensing (CS) takes advantage of a low-dimensional signal structure to reduce sampling requirements to far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transforms, finite differences, and low-rank extensions. Though powerful, these image priors are phenomenological in nature and do not account for the mechanism behind the image formation. On the other hand, MRI signal dynamics are governed by physical laws, which can be explicitly modeled and used as priors for reconstruction. These explicit and implicit signal priors can be synergistically combined in an inverse-problem framework to recover sharp, multicontrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, biophysical parameters from the data.