High-speed railway (HSR) communications are pivotal for ensuring rail safety, operations, maintenance, and delivering passenger information services. The high speed of trains creates rapidly time-varying wireless channels, increases the signaling overhead, and reduces the system throughput, making it difficult to meet the growing and stringent needs of HSR applications. In this article, we explore artificial intelligence (AI)-based beam-level and cell-level mobility management suitable for HSR communications, including the use cases, inputs, outputs, and key performance indicators (KPI)s of AI models. Particularly, in comparison to traditional down-sampling spatial beam measurements, we show that the compressed spatial multi-beam measurements via compressive sensing lead to improved spatial-temporal beam prediction. Moreover, we demonstrate the performance gains of AI-assisted cell handover over traditional mobile handover mechanisms. In addition, we observe that the proposed approaches to reduce the measurement overhead achieve comparable radio link failure performance with the traditional approach that requires all the beam measurements of all cells, while the former methods can save 50% beam measurement overhead.