The travelling salesperson problem (TSP) is one among the globally recognized and broadly studied problems and is known to be an NP-Hard problem in the field of operational research. It is a mathematical problem where one needs to find the shortest possible route in a collection of cities by passing through each one city exactly once. In order to solve this problem in polynomial time we don’t have any well suitable algorithm till date. Even though we have a variety of algorithms so far that provide near optimal solutions. To solve this problem two broad categories of algorithms are used so far one of the categories contains exact algorithms and the other one contains heuristic algorithms. In this paper we are going to review some of these algorithms which are given by different researchers in the past times and considered to be better approaches to solve this problem. To provide a better review we did a thorough analysis of these papers and came out with the brief introduction about the techniques/approaches used and their results.