This chapter discusses a number of generalizations of the Bernoulli random graph. The first is to Erdős–Rényi mixture models, in which each vertex belongs to one of a small number of distinct types, and the probability of an edge between two vertices being present depends on the types of the two vertices. Much as for the Bernoulli random graph, the neighbourhood structure is approximated by a multitype branching process. A threshold theorem for the existence of a giant component is derived, and the asymptotic proportions of the vertices in the giant component that belong to the different types is determined. Finally, the distribution of the length of the shortest path between two vertices of given types is approximated. The properties of some special network models of this kind, vertex weighted random graphs and bipartite networks, are examined. Another set of models considered is that of directed Bernoulli random graphs, in which there may be edges in either (or both) directions between any pair of vertices. Finally, Poissonized Erdős–Rényi mixture models for multigraphs are introduced, in which edges may be present between any pair of vertices, and the number of such edges has a Poisson distribution, with mean depending on the types of the vertices, the numbers being chosen independently. The extent to which these models differ from the standard Erdős–Rényi mixture models in the sparse regime is discussed.