The SUBLIMA project aims at truly simultaneous, fully integrated, solid-state PET/MR technology for concurrent functional and anatomical imaging with unsurpassed image quality. It will combine the extremely sensitive functional imaging possibilities provided by PET with the excellent soft-tissue contrast and complementary functional imaging capabilities of MR. For the first time, time-of-flight (ToF) and depth-of-interaction (DoI) correction will be introduced together into a PET/MR system. SUBLIMA will also be the first to exploit the unique advantages of truly simultaneous PET/MR acquisition by enabling fully 4D MR-derived motion correction. Furthermore, artefacts seen in PET-CT will be eliminated by developing MR-based, motion-compensated PET attenuation correction. The SUBLIMA platform will thus realize a breakthrough in image quality and enable novel applications in oncology, cardio-vascular medicine, and neuro-degenerative diseases. SUBLIMA will not only introduce new methods and technologies in each important component of the imaging chain, but it will also analyse the system performance as a function of all relevant design parameters, in order to push the image quality to the physical limits by optimally merging these innovations into 7T preclinical and 3T whole-body human demonstrator systems. This integrated approach also warrants adaptation of the project results for optimum performance in stand-alone PET and SPECT applications. The consortium, lead by Philips, consists of universities, research institutes, industrial partners, and SMEs, spread over 7 different countries including the USA. While each partner has shown exceptional quality in its own field, the consortium brings together the wide and complementary range of expertise necessary to push the performance of ToF-PET/MR to the physical limits.