The increasing uptake of converter-interfaced generation (CIG) is changing power system dynamics, rendering them extremely dependent on fast and complex control systems. Regularly assessing the stability of these systems across a wide range of operating conditions is thus a critical task for ensuring secure operation. However, the simultaneous simulation of both fast and slow (electromechanical) phenomena, along with an increased number of critical operating conditions, pushes traditional dynamic security assessments (DSA) to their limits. While DSA has served its purpose well, it will not be tenable in future electricity systems with thousands of power electronic devices at different voltage levels on the grid. Therefore, reducing both human and computational efforts required for stability studies is more critical than ever. In response to these challenges, several advanced simulation techniques leveraging artificial intelligence (AI) have been proposed in recent years. AI techniques can handle the increased uncertainty and complexity of power systems by capturing the non-linear relationships between the system’s operational conditions and their stability without solving the set of algebraic-differential equations that model the system. Once these relationships are established, system stability can be promptly and accurately evaluated for a wide range of scenarios. While hundreds of research articles confirm that AI techniques are paving the way for fast stability assessments, many questions and issues must still be addressed, especially regarding the pertinence of studying specific types of stability with the existing AI-based methods and their application in real-world scenarios. In this context, this article presents a comprehensive review of AI-based techniques for stability assessments in power systems. Different AI technical implementations, such as learning algorithms and the generation and treatment of input data, are widely discussed and contextualized. Their practical applications, considering the type of stability, system under study, and type of applications, are also addressed. We review the ongoing research efforts and the AI-based techniques put forward thus far for DSA, contextualizing and interrelating them. We also discuss the advantages, limitations, challenges, and future trends of AI techniques for stability studies.