The high penetration of renewable energy sources, coupled with decommissioning of conventional power plants, leads to the reduction of power system inertia. This has negative repercussions on the transient stability of power systems. The purpose of this paper is to review the state-of-the-art regarding the application of artificial intelligence to the power system transient stability assessment, with a focus on different machine, deep, and reinforcement learning techniques. The review covers data generation processes (from measurements and simulations), data processing pipelines (features engineering, splitting strategy, dimensionality reduction), model building and training (including ensembles and hyperparameter optimization techniques), deployment, and management (with monitoring for detecting bias and drift). The review focuses, in particular, on different deep learning models that show promising results on standard benchmark test cases. The final aim of the review is to point out the advantages and disadvantages of different approaches, present current challenges with existing models, and offer a view of the possible future research opportunities.