A number of laboratories and companies are currently exploring the development of integrated imaging systems for magnetic resonance imaging (MRI) and positron emission tomography (PET). Scanners for both preclinical and human research applications are being pursued. In contrast to the widely distributed and now quite mature PET/computed tomography technology, most PET/MRI designs allow for simultaneous rather than sequential acquisition of PET and MRI data. While this offers the possibility of novel imaging strategies, it also creates considerable challenges for acquiring artifact-free images from both modalities. This paper discusses the motivation for developing combined PET/MRI technology, outlines the obstacles in realizing such an integrated instrument, and presents recent progress in the development of both the instrumentation and of novel imaging agents for combined PET/MRI studies. The performance of the first-generation PET/MRI systems is described. Finally, a range of possible biomedical applications for PET/MRI are outlined.