Magnetic resonance imaging (MRI) is a medical imaging technology with fascinating capabilities. MRI is best understood as an universal computer-controlled sensing technology based on the physics of nuclear magnetic resonance. New techniques based on computational imaging developed during the last decade now start unlock its full potential. In these techniques data acquisition and reconstruction are jointly designed, integrating advanced signal models that accurately describe the physics of signal generation with new efficient sampling and measurement strategies. Recent methods also make optimal use of prior knowledge, e.g. using machine learning. New computational methods were not only used to speed up  conventional MRI scans but also enable completely new clinical and scientific applications. Important examples are real-time MRI of physiological processes such as the beating heart or the accelerated quantitative mapping of physical quantities, such as flow, diffusion, magnetic susceptibility, and much more.