Congestion in the transmission system is one of the major emerging problems in the power system. Due to congestion, there is always a probability of grid failure and voltage collapse which can lead to blackout in the system. Various methods and approaches have been considered to eliminate the problem of congestion within the required time so that we can ensure the safe operations of the system and prevent the occurrence of various abnormalities in the system. Several challenges have arisen to solve the problem of congestion like complex system, uncertainty associated with predicting demand and capacity, coordination among multiple stakeholders, cost of the investment in infrastructure and technology, etc. However, many optimization techniques are successfully implemented to manage the above problems including the concept of the Shapley value which is based on the cooperative game theory. This idea deals with the allocation of congestion cost among various consumers on the basis of their marginal contribution in terms of load in the system. Various limitations regarding the system are taken into consideration while designing a model or developing a methodology to manage the problem of the congestion in the power system. This paper presents an overview of various congestion management methods like generation re-scheduling which mainly focuses on generator sensitivity characteristics to ensure the economic operation of the system, Flexible AC Transmission Systems (FACTSs) devices are utilized to compensate the reactive power, Distributed Generation (DG) strategies are applied for lowering of line congestion by allocating the suitable DGs of different capacities, and other Market-Based Congestion Management (MBCM) strategies also have been proposed. In the end, the concept of Shapley value has been addressed to fairly distribute the cost among different consumers.