Heavy ion fusion research at GSI is dedicated to accelerator experimen
ts and theory in the r.f. linac-storage ring approach as well as exper
imental work in ion beam focusing and ion beam plasma interaction. The
status of the accelerator-based work is summarized in this paper. Imp
ortant topics along this line have been the studies on the European Ig
nition Facility, high current development at the SIS and beam target e
xperiments, experimental and theoretical studies on the longitudinal r
esistive instability, bunched beam experiments using a streak camera a
s well as theoretical work on resonance crossing.