The node degrees of large real-world networks often follow a power-law distribution. Such scale-free networks can be social networks, internet topologies or many other networks. There is, however, no established and simple network model which also has a high clustering of vertices as typically observed in real data. The first part of the talk will present several mathematical models of scale-free networks and introduce hyperbolic random graphs as a natural model that fulfills most properties of real world networks. The second part will show how to efficiently embed networks in the hyperbolic space and analyze some algorithms on hyperbolic random graphs.