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It is vital to obtain a good description of the Internet topology because structure fundamentally affects function. This paper reviews two recent achievements on characterising and modelling the Internet topology at the autonomous systems level, including a newly discovered structure, called the rich-club phenomenon, and one of the most successful Internet topology generators to date, the positive-feedback preference (PFP) model. The discovery of the rich-club phenomenon is significant because an appreciation of this hierarchy structure is essential for a proper examination of the global Internet properties, such as routing efficiency, network flexibility and robustness. The PFP model accurately reproduces the largest set of important topology characteristics of the Internet. The model can be used for more realistic simulation studies of the Internet. The model also provides novel insights into the underlying rules that govern the Internet evolution.