The problem of the scalability of inter-domain routing is of the main issues in the design of Next Generation Internet (NGI). This paper addresses the intrinsic essences of the problems created by the scalability of Internet routing by introducing the entropy routing information concept. Based on the theoretical model of entropy in routing information, potential solutions to the routing scalability problems are discussed, which focus on three different aspects with their respective benefits and limitations and their architectural evaluations on typical proposals. In the end, a conclusion on the challenges of the Internet routing scalability problem is drawn, and the direction of further research on this problem is explored.