Hybrid inverse problems, also called coupled-physics inverse problems, aim to leverage the physical coupling between a high-contrast, low-resolution, modality and a low-contrast, high-resolution, modality to obtain a high- contrast, high-resolution, imaging procedure. From a mathematical standpoint, several such procedures involve the reconstruction of parameters from internal functionals of said parameters and solutions to partial differential equations. This talk will review several theoretical analyses and numerical results obtained recently in the field of hybrid inverse problems. Applications include the biomedical imaging modalities called Quantitative Photo-Acoustic Tomography, Transient and Magnetic Resonance Elastography, and Ultrasound Modulated Tomography.