Condition monitoring of rail transport systems has become a phenomenon of global interest over the past half a century. The approaches to condition monitoring of various rail transport systems—especially in the context of rail vehicle subsystem and track subsystem monitoring—have been evolving, and have become equally significant and challenging. The evolution of the approaches applied to rail systems’ condition monitoring has followed manual maintenance, through methods connected to the application of sensors, up to the currently discussed methods and techniques focused on the mutual use of automation, data processing, and exchange. The aim of this paper is to provide an essential overview of the academic research on the condition monitoring of rail transport systems. This paper reviews existing literature in order to present an up-to-date, content-based analysis based on a coupled methodology consisting of bibliometric performance analysis and systematic literature review. This combination of literature review approaches allows the authors to focus on the identification of the most influential contributors to the advances in research in the analyzed area of interest, and the most influential and prominent researchers, journals, and papers. These findings have led the authors to specify research trends related to the analyzed area, and additionally identify future research agendas in the investigation from engineering perspectives.