This paper presents a systematic literature survey on diagnostic methods used for railway materials and systems. The authors analyze various railway accident reports, focusing on the types of failures described and their causes. Previous review papers have addressed various aspects of railway systems diagnostics; however, most of the existing research focuses on specific parts of the rail vehicle or subsystems. In contrast, this survey focuses on railway diagnostic systems rather than general diagnostic methods used in mechanical and electrical engineering. The authors classify the types of failures and diagnostic methods that are used in rail transport into two categories: infrastructure and rolling stock. The purpose of this paper is to systematize the types of failure that occur in railway transport systems; identify the state-of-the-art means and methods of diagnostics in railway materials and systems, with particular focus on new research findings; and identify trends and possible research gaps in need of further development.