An autonomous system is a network or group of networks under a common administration and with common routing policies. The Internet is a collection of such autonomous systems. In order to find a path from one autonomous system to any other autonomous system, neighboring autonomous systems exchange routing information via the Border Gateway Protocol. However, BGP suffers from several types of divergence anomalies. A divergence anomaly occurs when BGP routers permanently fail to obtain a stable path to reach a destination autonomous system. In this paper the different types of BGP divergence anomalies are discussed, along with their proposed solutions.