Theoretical studies present a quite detailed view of the stability of nuclei in the region of the heaviest elements. Three regions of increased stability exist. Two for deformed nuclei at proton and neutron numbers Z = 100 and N = 152 and at Z = 108 and N = 162. The third region is located at Z = 114, 120 or 126 and N = 184 for spherical nuclei due to closed shells or subshells. Experimentally, the existence of these regions of increased stability is established by synthesis of nuclei in cold fusion reactions using lead or bismuth targets and in hot fusion reactions based on actinide targets. Present experiments are trying to consolidate existing data and to explore the extension of the island of spherical nuclei into the direction of still heavier elements. The present status of experiments at the GSI SHIP is given as well as an outlook on investigations planned for the near future.