AbstractHeavy ion fusion research at GSI is dedicated to accelerator experiments and theory in the r.f. linac-storage ring approach as well as experimental work in ion beam focusing and ion beam plasma interaction. The status of the accelerator-based work is summarized in this paper. Important topics along this line have been the studies on the European Ignition Facility, high current development at the SIS and beam target experiments, experimental and theoretical studies on the longitudinal resistive instability, bunched beam experiments using a streak camera as well as theoretical work on resonance crossing.