Formal methods and verification tools have been in use in the engineering of safety-critical transport systems for well over 30 years. In both the railway and the avionics domain, for instance, formal methods are specifically recommended in current international certification standards for ultra-dependable systems and for products at the highest integrity level. In fact, traditionally, the applications of formal methods and tools to such transport systems concern demonstrating, with the highest levels of assurance, the correct functioning of the software systems involved, such as train signalling systems to avoid collisions. More recently, however, formal methods and verification tools have started to be applied also to the scheduling and management of transport systems or networks, for instance to optimise the exploitation of a railway line or to improve the operational efficiency of a bus network. In this introduction to the special issue on "Formal Methods for Transport Systems", we outline some recent achievements for each of the above-mentioned types of application of formal methods and tools. These achievements are represented by three selected papers: one was selected from the "Formal Methods and Safety Certification: Challenges in the Railways Domain" track at the seventh International Symposium On Leveraging Applications of Formal Methods, Verification and Validation (ISoLA 2016); another one was selected from the 21st International Workshop on Formal Methods for Industrial Critical Systems and the 16th International Workshop on Automated Verification of Critical Systems (FMICS-AVoCS 2016); a final one was selected after an open call for contributions.