This review concentrates on the specific properties and characteristics of damage structures generated with high-energy ions in the electronic energy loss regime. Irradiation experiments with so-called swift heavy ions (SHI) find applications in many different fields, with examples presented in ion-track nanotechnology, radiation hardness analysis of functional materials, and laboratory tests of cosmic radiation. The basics of the SHI-solid interaction are described with special attention to processes in the electronic subsystem. The broad spectrum of damage phenomena is exemplified for various materials and material classes, along with a description of typical characterization techniques. The review also presents state-of-the-art modeling efforts that try to account for the complexity of the coupled processes of the electronic and atomic subsystems. Finally, the relevance of SHI phenomena for effects induced by fission fragments in nuclear fuels and how this knowledge can be applied to better estimate damage risks in nuclear materials is discussed.