High-speed railway (HSR) communications will become a key feature supported by intelligent transportation communication systems. The increasing demand for HSR communications leads to significant attention on the study of radio resource management (RRM), which enables efficient resource utilization and improved system performance.RRM design is a challenging problem due to heterogenous quality of service (QoS) requirements and dynamic characteristics of HSR wireless communications. The objective of this paper is to provide an overview on the key issues that arise in the RRM design for HSR wireless communications. A detailed description of HSR communication systems is first presented, followed by an introduction on HSR channel models and characteristics, which are vital to the cross-layer RRM design. Then we provide a literature survey on state-of-the-art RRM schemes for HSR wireless communications, with an in-depth discussion on various RRM aspects including admission control, mobility management, power control and resource allocation. Finally, this paper outlines the current challenges and open issues in the area of RRM design for HSR wireless communications.