Border Gateway Protocol (BGP), a path vector routing protocol, is a widespread exterior gateway protocol (EGP) in the internet. Extensive deployment of the new technologies in internet, protocols need to have continuous improvements in its behavior and operations. New routing technologies conserve a top level of service availability. Hence, due to topological changes, BGP needs to achieve a fast network convergence. Now a days size of the network growing very rapidly. To maintain the high scalability in the network BGP needs to avoid instability. The instability and failures may cause the network into an unstable state, which significantly increases the network convergence time. This paper summarizes the various approaches like BGP policies, instability, and fault detection etc. to improve the convergence time of BGP.