The integration of positron emission tomography (PET) and magnetic resonance imaging (MRI) has been an ongoing research topic for the last 20 years. This paper gives an overview of the different developments and the technical problems associated with combining PET and MRI in one system. After explaining the different detector concepts for integrating PET-MRI and minimising interference the limitations and advantages of different solutions for the detector and system are described for preclinical and clinical imaging systems. The different integrated PET-MRI systems are described in detail. Besides detector concepts and system integration the challenges and proposed solutions for attenuation correction and the potential for motion correction and resolution recovery are also discussed in this topical review.