Reactor physics is the study of neutron properties, focusing on using models to examine the interactions between neutrons and materials in nuclear reactors. Artificial intelligence (AI) has made significant contributions to reactor physics, e.g., in operational simulations, safety design, real-time monitoring, core management and maintenance. This paper presents a comprehensive review of AI approaches in reactor physics, especially considering the category of Machine Learning (ML), with the aim of describing the application scenarios, frontier topics, unsolved challenges and future research directions. From equation solving and state parameter prediction to nuclear industry applications, this paper provides a step-by-step overview of ML methods applied to steady-state, transient and combustion problems. Most literature works achieve industry-demanded models by enhancing the efficiency of deterministic methods or correcting uncertainty methods, which leads to successful applications. However, research on ML methods in reactor physics is somewhat fragmented, and the ability to generalize models needs to be strengthened. Progress is still possible, especially in addressing theoretical challenges and enhancing industrial applications such as building surrogate models and digital twins.