© 2020 The Author(s). Background: The targeting accuracy of proton therapy (PT) for moving soft-tissue tumours is expected to greatly improve by real-time magnetic resonance imaging (MRI) guidance. The integration of MRI and PT at the treatment isocenter would offer the opportunity of combining the unparalleled soft-tissue contrast and real-time imaging capabilities of MRI with the most conformal dose distribution and best dose steering capability provided by modern PT. However, hybrid systems for MR-integrated PT (MRiPT) have not been realized so far due to a number of hitherto open technological challenges. In recent years, various research groups have started addressing these challenges and exploring the technical feasibility and clinical potential of MRiPT. The aim of this contribution is to review the different aspects of MRiPT, to report on the status quo and to identify important future research topics. Methods: Four aspects currently under study and their future directions are discussed: modelling and experimental investigations of electromagnetic interactions between the MRI and PT systems, integration of MRiPT workflows in clinical facilities, proton dose calculation algorithms in magnetic fields, and MRI-only based proton treatment planning approaches. Conclusions: Although MRiPT is still in its infancy, significant progress on all four aspects has been made, showing promising results that justify further efforts for research and development to be undertaken. First non-clinical research solutions have recently been realized and are being thoroughly characterized. The prospect that first prototype MRiPT systems for clinical use will likely exist within the next 5 to 10 years seems realistic, but requires significant work to be performed by collaborative efforts of research groups and industrial partners.