The Internet routing system is facing a serious scaling challenge due to the rapid growth of the global routing table. For the purpose of reducing routing table size, many studies have developed a lot of new routing solutions. After the paper introduces the background of the Internet routing system, a classification of new routing solutions is presented. Then, a typical scalable routing algorithms and architectures become the focus, and their basic ideas and characteristics are deeply analyzed and compared. Finally, some key issues and ideas for future research are discussed.