The combination of PET and MR in one imaging device has certain advantages over conventional imaging modalities. These include: no additional radiation dose from the MR, superior soft tissue contrast and a multitude of tracers for PET. Certain technical challenges exist when designing a PET/MR system. On the one hand these stem from the presence of the strong MR magnetic field and the addition of PET components to the MR system. Different approaches are presented to overcome these technical obstacles ranging from long optical fibers to systems that use semiconductor light detectors for photon counting. The applications of combined PET/MR are profound in the field of oncology and allow imaging of the four main processes in cancer formation: apoptosis resistance, angiogenesis, proliferation and metastasis. PET/MR has also many clinical and research applications in neurology and cardiology. Alternative techniques such as image fusion, hyperpolarized imaging, 17O imaging and whole body diffusion are discussed in respect to their relevance regarding PET/MR. Simultaneous multifunctional and anatomical imaging using PET/MR has a great potential to impact biomedical imaging in research and clinic.