The development of integrated imaging systems for magnetic resonance imaging (MRI) and positron emission tomography (PET) is currently being explored in a number of laboratories and industrial settings. PET/MRI scanners for both preclinical and human research applications are being developed. PET/MRI overcomes many limitations of PET/computed tomography (CT), such as limited tissue contrast and high radiation doses delivered to the patient or the animal being studied. In addition, recent PET/MRI designs allow for simultaneous rather than sequential acquisition of PET and MRI data, which could not have been achieved through a combination of PET and CT scanners. In a combined PET/CT scanner, while both scanners share a common patient bed, they are hard-wired back-to-back and therefore do not allow simultaneous data acquisition. While PET/MRI offers the possibility of novel imaging strategies, it also creates considerable challenges for acquiring artifact-free images from both modalities. In this review, we discuss motivations, challenges, and potential research applications of developing PET/MRI technology. A brief overview of both MRI and PET is presented and preclinical and clinical applications of PET/MRI are identified. Finally, issues and concerns about image quality, clinical practice, and economic feasibility are discussed.