The integration of positron emission tomography (PET) and magnetic resonance imaging (MRI) in a combined PET/MR scanner is attracting much interest. With this new bimodal approach novel functional-anatomical and multiparametric applications become feasible, which can be expected to deliver information beyond that accessible by separately applied modalities. Although the two technologies where initially regarded as inherently incompatible, different solutions have been developed and implemented to realise PET/MR instruments for both small animal and human bimodal imaging. The present review first summarizes the basic options for possible PET/MR designs. A chronological outline describes the evolution from the first ideas, how PET and MR imaging might be combined, over different experimental solutions to the systems recently realized by industry. The BrainPET/MR and the mMR developed by Siemens and the Philips Ingenuity TF PET/MR are characterised and application examples are provided illustrating the features of these instruments. Based on own experiences and those reported in different publications a number of open issues are discussed. Finally a short comparative analysis on the status and perspectives of human PET/MR imaging is given.