Multimodal imaging is now well-established in routine clinical practice. Especially in the field of nuclear medicine, new positron emission tomography (PET) installations comprise almost exclusively combined PET/computed tomography (CT) scanners rather than PET-only systems. However, PET/CT has certain notable shortcomings, including the inability to perform simultaneous data acquisition and the significant radiation dose to the patient contributed by CT. Magnetic resonance imaging (MRI) offers, compared with CT, better contrast among soft tissues as well as functional-imaging capabilities. Therefore, the combination of PET with MRI provides many advantages that go far beyond simply combining functional PET information with structural MRI information. Many technical challenges, including possible interference between these modalities, have to be solved when combining PET and MRI, and various approaches have been adapted to resolving these issues. Here, we present an overview of current working prototypes of combined PET/MRI scanners from different groups. In addition, besides PET/MRI images of mice, the first such images of a rat acquired with the first commercial clinical PET/MRI scanner, are presented. The combination of PET and MRI is a promising tool in preclinical research and will certainly progress to clinical application.