The integration of variable renewable energy sources (RES) into power grids has resulted in a more complex operating environment for power system operators (SO), necessitating the need for increased grid flexibility. This is crucial for utilities, as the cost-effective utilization of existing infrastructure is necessary, given the prolonged construction period and high investment costs associated with building new power delivery facilities. Under the umbrella of smart grid, optimal transmission switching (OTS) is a cost-effective transmission technology that can alleviate concerns related to network congestion, limited transmission capacity, and high penetration of renewables. OTS is a concept that is integrated into the optimal power flow (OPF) problem such that it provides SO the choice to temporarily switch one or more lines out of service from the network. OTS is shown in the literature to have economic benefits, reduce operational cost, relieve network congestion, serve as a corrective mechanism for reducing voltage violations, improve system reliability, and minimize system loss. Despite the significant attention given to OTS by researchers over the past decade, no extensive review paper exists on the topic in the literature. Therefore, this paper provides a state-of-the-art overview of the OTS problem. The concept of OTS is explained by approximating the alternating current OPF problem into a linear direct current OPF problem. Various alternative models of the OTS problem proposed in the literature are discussed. The paper also analyzes the interaction between OTS and other flexibility options such as Dynamic thermal rating (DTR), Energy storage systems (ESS), and RES. Furthermore, the paper presents the general framework and impact of the short-term OTS problem on long-term expansion planning problems. Finally, an extensive literature review on the impact of OTS on system reliability is provided.