Offshore geological hazards can occur in any marine domain or environment and represent a serious threat to society, the economy, and the environment. Seismicity, slope sedimentary instabilities, submarine volcanism, fluid flow processes, and bottom currents are considered here because they are the most common hazardous processes; tsunamis are also examined because they are a secondary hazard generated mostly by earthquakes, slope instabilities, or volcanic eruptions. The hazards can co-occur and interact, inducing a cascading sequence of events, especially in certain contexts, such as tectonic indentations, volcanic islands, and canyon heads close to the coast. We analyze the key characteristics and main shortcomings of offshore geological hazards to identify their present and future directions for marine geoscience investigations of their identification and characterization. This review establishes that future research will rely on studies including a high level of multidisciplinarity. This approach, which also involves scientific and technological challenges, will require effective integration and interplay between multiscale analysis, mapping, direct deep-sea observations and testing, modelling, and linking offshore observations with onshore observations.