Since the appearance of mechanized rail transport systems in England in the 1820s, the railway has evolved as an essential service and has become the primary mode of long-distance land transportation for people as well as for bulk material across the world. It is essential for every railway organization to maintain high quality of service to not only differentiate itself and create a competitive edge over other modes of transport but also to survive. Factors such as speed, reliability, passenger comfort, convenience, system safety, special services, innovations, efficiency, itinerary accuracy and so on are important to ensure satisfactory services. The locomotive assignment problem (LAP) is one problem which, if addressed properly, would go a long way to improve the quality of services provided by the railway organization. In this work, we thoroughly study the literature pertaining to LAP to identify the constraints that have been considered hitherto by various authors. We also try to single out constraints that are relevant but ignored by most of the studies. Finally, we review studies that are specific to the Indian context and highlight the scope for further work.