As the basis of Internet development and exploitation on higher levels, the Internet topology modeling starts from the random model to the hierarchical model. Then it developed to a more realistic one, scale-free network model. Many characteristics of topology are analyzed with the corresponding metrics, including power law. Moreover, the related work on the current topology models, topology generation algorithms, and topology generators is fully presented. Finally, the new problems and challenges which arise from current research are discussed and some suggestions for future research work are put forward.