It is well-known that large-scale networks in the real world seem to lack a regular, well-defined pattern or structure. In order to model such networks, many inhomogeneous random graphs have been introduced and studied. This paper is a survey of many classes of random graphs which are mathematically treatable, such as edge-independent graphs or sparse inhomogeneous models. Some results concern random subgraphs obtained by a Bernoulli selection of edges and the associated phase transition. The branching process approach to the study of random graphs is widely used in the whole paper to prove results on classical homogeneous and inhomogeneous graphs. The authors highlight immediately the importance of the branching process approach: on one hand many sharp results in the classical case admit simpler proofs with this technique, on the other hand it can be applied to sparse inhomogeneous random graphs to obtain analogous (but often necessarily weaker) results. This approach can be used to study many aspects of random graphs including (but not limited too) phase transition phenomena. Many simple classical models are not well suited to mimic real world networks since they have fairly flat distributions of degrees which is in contrast with the real situation where power-law distributions are often observed (scale-free networks). Hence, after discussing the classical models, the paper focuses on scale-free inhomogeneous models, in particular sparse graphs. Many of these models, though very detailed, are too complicate to allow a rigorous mathematical analysis and must be studied by simulations. The last part of the paper is devoted to the question of the choice of the right model which fits better a given situation (this raises questions about metrics on graphs).