Efficiency in the public and freight transportation systems is of crucial importance for a society. Railways can offer high capacity and relatively low environmental impact, but require that several technical systems are tuned and operate well. Specifically there is a very tight interdependency between infrastructure and trains, which distinguishes railways from other transportation modes. Thus maintenance of all the subsystems is needed. Railways do also have some specific and complicating properties that influence maintenance and operations: Most activities need exclusive access to the infrastructure and - due to the geographic layout, safety requirements and partitioning of the subsystems - large portions of the network will be affected by each activity. Furthermore, several organisational units and resources are involved, ranging from governments and regulatory bodies, over operators and contractors to suppliers, technical experts and work forces. Thus railway maintenance is complicated to organize and consumes large budgets. This thesis treats the planning and scheduling problems that concern railway infrastructure maintenance and the coordination with train traffic. Mathematical methods and optimization are studied and used, with the aim of advancing the knowledge about models for solving such problems. The thesis contains three papers and presents: (1) A survey regarding railway maintenance activities, the major planning problems and the conducted research so far; (2) A model for quantitative comparison and assessment of competing capacity requests from train operations and maintenance; (3) An optimization model for integrated scheduling of both maintenance windows and train services. The work can be helpful for practitioners as well as researchers who want to take further steps in this interesting and challenging area. Based on the results that have been obtained, future research directions are presented that may lead towards practical use of concurrent planning of railway maintenance and train services.