The combination of several imaging modalities into a hybrid device has enabled a straightforward and accurate solution for the investigation of multiparametric processes in vivo. All existing imaging modalities have both strengths and weaknesses. For instance, computed tomography (CT) is an excellent modality for imaging bones. Magnetic resonance tomography images the effects of a manifold of interaction mechanisms between the spin ensemble and/with its environment and other nuclei. The differences in these interactions depend much more on the tissue type, its microscopic environment and interactions at the quantum level and therefore MR images provide a wide variety of superior soft tissue contrasts. Gamma scintigraphy, single photon emission computed tomography and positron emission tomography detect single radioactive decays from tagged molecules and can infer the spatial position of the decays from a few thousand decays. Thus, the sensitivity of these modalities is very high, but the spatial resolution is very low. Instead of pushing CT and MRI technology towards molecular imaging and positron emission tomography (PET) technology towards structural imaging, a much more promising approach is to further optimise the strengths of these modalities by combining them into hybrid devices. The combination of MRI and PET has been the second bi-modality, which resulted in commercially available hybrid scanners for animal and human imaging. In this chapter, the most important mutual interferences of PET and MRI, together with technical solutions for minimising them, are presented and discussed.