In fission and fusion of heavy nuclei large numbers of nucleons are rearranged at a scale of excitation energy very small compared with the binding energy of the nuclei. The energies involved are less than 40 MeV at nuclear temperatures below 1.5 MeV. The shapes of the configurations in the rearrangement of a binary system into a monosystem in fusion, or vice versa in fission, change their elongations by as much as 8 fm, the radius of the monosystem. The dynamics of the reactions macroscopically described by a potential energy surface, inertia parameters, dissipation, and a collision energy is strongly modified by the nuclear structure of the participating nuclei. Experiments showing nuclear structure effects in fusion and fission of the heaviest nuclei are reviewed. The reaction kinematics and the multitude of isotopes involved are investigated by detector techniques and by recoil spectrometers. The advancement of the latter allows one to find very small reaction branches in the range -. The experiments reveal nuclear structure effects in all stages of the rearrangement processes. These are discussed, pointing to analogies in fusion and fission on the microscopic scale, notwithstanding that both processes macroscopically are irreversible. Heavy clusters, as , , nuclei with closed-shell configurations N = 82, 126, Z = 50, 82 survive in large parts of the nuclear rearrangement. They determine the asymmetry in the mass distribution of low-energy fission, and they allow the synthesis of superheavy elements, currently up to element 112. Experiments on the cold rearrangement in fission and fusion are presented. Here, in the range of excitation energies below 12 MeV, the phenomena are observed most convincingly.