The Internet topology at the autonomous systems (AS) level exhibits a complex structure. The positive-feedback preference (PFP) model was designed to capture two properties of the Internet, namely the degree distribution and the rich-club connectivity. It has been a pleasant surprise that the model also reproduces a large number of other properties of the Internet, including the degree correlation, the triangle coefficient, the shortest path length etc. Here we explain that the success of the PFP model is due to the inherent structural constraints present in the Internet topology. This work advances our understanding of the Internet structure. It also highlights the importance for a network model to choose carefully its target properties. For example, as we show, an Internet model based on the degree distribution only could produce network structures completely different from the real Internet. ©2008 IEEE.