Railway transportation has been around for decades and has seen a massive shift in its paradigm in terms of planning and implementation of timetable and rules. Railways are a part of millions of people’s everyday lives and this has seen a change from a few railway lines to large companies that deal with the planning and services of said railway. We have selected this topic not only to see how mathematical solutions compare far better than manual planning but to also observe the change in the intricacies of the working of railways through operations research. Operations Research is the application of scientific methods to problems arising from operations involving integrated systems of people, machines and materials. In a nut shell, it is the discipline of applying appropriate analytical methods to help make better decisions with the help of practitioners, researchers, educators, and students which have an ecosystem of strengths, weaknesses, opportunities and threats. Some areas OR can be applicable are Line capacity estimation, Strategic problems, Capacity planning (infrastructure), Tactical problems. It is also used in operational problems such as train control, dynamic scheduling & dynamic pricing. Researchers and practitioners alike have applied many techniques in Transportation sector, for both tactical as well as operational issues. There is still tremendous scope for application of OR techniques to optimize the Railway Operations.In this paper we give an overview of state-of-the-art Operations Research models and techniques used in passenger railway transportation. For each planning phase (strategic, tactical and operational), we hope to describe the planningproblems arising there and discuss some models and algorithms to solve them. We not only consider classical, well-known topics such as timetabling, rolling stock scheduling and crew scheduling, but we will also discuss some recently developed topics such as shunting and reliability of timetables. Finally, we will focus on several practical aspects for each of these problems. There is a lot of scope for research in this field with real time data. Indian Railways can see massive change in their functioning and effectiveness if Operations Research methods are applied on a large scale. Optimization tools have improved with the increased computational power and it will now be possible to solve many problems which seemed difficult or impossible before.