With the widespread deployment of high-speed railways and the increasing speed of trains, timely and reliable wireless transmission of train control signals and passengers' mobile Internet access become critical. To meet these demands, mobile communication systems for railways is shifting from narrowband global system for mobile communications-railway (GSM-R) to broadband systems. In contrast to GSM-R, broadband LTE-R and 5G for railway system could provide more services such as real-time video surveillance, multimedia dispatching and railway Internet of Things. In this paper, we first briefly review the existing GSM-R system and discuss its limitations. Then, we discuss future development of user demands and various data services, which suggests the key performance indicators of the future mobile communication systems for railways. Afterwards, we survey the recent wireless technologies and network architectures that may be applied in mobile communication systems for railways in the near future. Finally, we summarize the technical challenges of future mobile communication systems for railways and conclude this paper.