Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learning-based MRI reconstruction. We consider inverse problems with both linear and nonlinear forward models for computational MRI and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play (PnP) methods, generative models, and unrolled networks. We highlight domain-specific challenges, such as real- and complex-valued building blocks of neural networks, and translational applications in MRI with linear and nonlinear forward models. Finally, we discuss common issues and open challenges, and we draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline.