The secure operation of the transmission grid is of primary importance for any power system operator. However, the introduction of new technologies, market deregulation, and increasing levels of interconnectivity have made the analysis and assessment of power system security both more challenging and essential than ever. In this context, data-driven-based methodologies are being increasingly employed to classify and anticipate insecure future states, and make inferences on potential triggers of undesired operational conditions. This paper provides a comprehensive and systematic review of this fast-moving research area and covers data-driven-based methodologies deployed in both static and dynamic security assessment. Particular attention is paid to recent trends, such as the use of spatiotemporal feature selection algorithms and the increasing research activity in short-term voltage stability and frequency stability, which are not yet widely assessed as a collective in the existing literature.