Formal methods are mathematically-based techniques for the rigorous development of software-intensive systems. The railway signaling domain is a field in which formal methods have traditionally been applied, with several success stories. This article reports on a mapping study that surveys the landscape of research on applications of formal methods to the development of railway systems. Our main results are as follows: (i) we identify a total of 328 primary studies relevant to our scope published between 1989 and 2020, of which 44% published during the last 5 years and 24% involving industry; (ii) the majority of studies are evaluated through Examples (41%) and Experience Reports (38%), while full-fledged Case Studies are limited (1.5%); (iii) Model checking is the most commonly adopted technique (47%), followed by simulation (27%) and theorem proving (19.5%); (iv) the dominant languages are UML (18%) and B (15%), while frequently used tools are ProB (9%), NuSMV (8%) and UPPAAL (7%); however, a diverse landscape of languages and tools is employed; (v) the majority of systems are interlocking products (40%), followed by models of high-level control logic (27%); (vi) most of the studies focus on the Architecture (66%) and Detailed Design (45%) development phases. Based on these findings, we highlight current research gaps and expected actions. In particular, the need to focus on more empirically sound research methods, such as Case Studies and Controlled Experiments, and to lower the degree of abstraction, by applying formal methods and tools to development phases that are closer to software development. Our study contributes with an empirically based perspective on the future of research and practice in formal methods applications for railways.