This paper surveys related research work of Internet overlay routing, and focuses on the structure and methods of Internet overlay routing on network layer and transport layer according to Internet layering scheme. Apart from that, other related aspects of overlay routing are discussed, including the impacts on overlay routing performance, and interactions between multiple overlay networks routing, etc. The advantages and disadvantages in the key technologies of related research work are analyzed. At last, the possible future research directions are discussed as references for the research of Internet overlay routing.