Instruments that combine positron emission tomography (PET) and magnetic resonance (MR) imaging have recently been assembled for use in humans, and may have diagnostic performance superior to that of PET/computed tomography (CT) for particular clinical and research applications. MR imaging has major strengths compared with CT, including superior soft-tissue contrast resolution, multiplanar image acquisition, and functional imaging capability through specialized techniques such as diffusion-tensor imaging, diffusion-weighted (DW) imaging, functional MR imaging, MR elastography, MR spectroscopy, perfusion-weighted imaging, MR imaging with very short echo times, and the availability of some targeted MR imaging contrast agents. Furthermore, the lack of ionizing radiation from MR imaging is highly appealing, particularly when pediatric, young adult, or pregnant patients are to be imaged, and the safety profile of MR imaging contrast agents compares very favorably with iodinated CT contrast agents. MR imaging also can be used to guide PET image reconstruction, partial volume correction, and motion compensation for more accurate disease quantification and can improve anatomic localization of sites of radiotracer uptake, improve diagnostic performance, and provide for comprehensive regional and global structural, functional, and molecular assessment of various clinical disorders. In this review, we discuss the historical development, software-based registration, instrumentation and design, quantification issues, potential clinical applications, potential clinical roles of image segmentation and global disease assessment, and challenges related to PET/MR imaging.