With the continued expansion of urban rail transit networks and the increasing complexity of operating scenarios, passenger demand exhibits more complex spatiotemporal patterns, posing higher requirements for train operation organization and passenger flow control. Short-term passenger flow prediction is an important basis for urban rail transit operation management and provides key support for operational decision-making. In recent years, artificial intelligence-based methods have become an important technical approach for improving short-term passenger flow prediction performance, owing to their strong capability to extract complex spatiotemporal features. This review focuses on artificial intelligence-based methods for short-term passenger flow prediction in urban rail transit systems. It first constructs a task analysis framework from five dimensions: prediction scenarios, prediction targets, data sources, prediction methods, and evaluation metrics. Second, the development trajectory of prediction models is systematically reviewed. Furthermore, recent studies and major challenges are summarized for different prediction tasks, including station inflow and outflow passenger flow prediction, origin-destination passenger flow prediction, section passenger flow prediction, multi-type passenger flow collaborative prediction, and multimodal traffic prediction with rail transit as the backbone. Finally, future research directions are discussed from the perspectives of large language models, trustworthy and interpretable prediction, an end-to-end predict-and-optimize learning framework, and world models. This review shows that short-term passenger flow prediction in urban rail transit is evolving from single-flow-type, single-metric, and single-task prediction toward integrated development featuring multi-source perception, multi-type passenger flow collaboration, and multi-metric evaluation. Future research should further emphasize general adaptability, uncertainty awareness, trustworthy risk assessment, decision-oriented prediction, and world-model-driven dynamic deduction, with the aim of building an integrated intelligent prediction and simulation framework for complex operational scenarios and supporting refined operational decision-making in urban rail transit.