Atomically flat terraces of the Re(0001) surface with a contaminant density below 0.5% have been obtained by oxygen annealing followed by a flash to higher temperature. This Re(0001) single crystal has been used as a substrate for the deposition of Fe, Co and Cr atoms. Scanning Tunneling Microscopy experiments characterize the growth mode for the submonolayer coverage regime. Co, Cr and Fe atoms self-assemble to form monolayer high islands. Despite a large lattice mismatch between film and substrate, Co and Fe grow pseudomorphically up to half a monolayer. Cr islands are pseudomorphic only for a size below 10 nm. Higher coverage leads to reconstructed islands with an element-dependent reconstruction pattern. Scanning Tunneling Spectroscopy measurements at 8 K reveal the electronic properties of Fe and Re. Differential conductance measurements on the Re(0001) show the presence of standing waves, possibly due to a rhenium surface state. Atomic resolution images of Fe attached to a Re step edge lead to the conclusion that the Fe atoms occupy hcp hollow sites. A Néel magnetic ordered state of the Fe hcp monolayer is revealed with Spin-Polarized Scanning Tunneling Microscopy and Magnetic Atom Manipulation Imaging.