Positron emission tomography/magnetic resonance imaging (PET/MR) is a new multi-modality imaging technique allowing a simultaneous acquisition of PET and MR images leading to a fusion of anatomical and functional information. There are currently challenges associated with the use of MR for the correction of different effects reducing overall PET image qualitative and quantitative accuracy such as scatter, attenuation, and partial volume effects. Moreover the fusion accuracy of functional and anatomical information may be compromised by patient respiratory motion. Respiratory motion is an important source of medical image degradation and artifacts, compromising accurate quantitation in thoracic and abdominal imaging studies. In addition, the uncertainties resulting from breathing hinder the localization of internal structures in these body regions, and are still today a major limitation in external beam radiotherapy treatment planning and delivery. Intra and inter fraction motion are not fully handled in current clinical practice, except by the addition of margins that lead to sub-optimal irradiation by decreasing the dose received by the tumor and increasing the dose received by the surrounding healthy tissues and organs at risk. This is due to the lack of appropriate tools and methods that are currently limited to 1D respiratory motion characterization based on the information from a very small part of the thorax for intra-fraction, and invasive and ionizing imaging techniques for inter-fraction motion management. This lecture will handle the issues and solutions in PET/MR and in radiotherapy with a special focus on respiratory motion management.