This chapter considers settings in which networks are used in statistical inference. First, there is often dependence between measurements taken at vertices of a network, with vertices at small graph distance more highly dependent. Methods for accommodating such dependence, including network effects and network disturbance models, are discussed. In such cases, the network is treated as a nuisance parameter. In contrast, the network itself may be the object of primary interest. Fitting a model to the network may make possible inference, for instance about the presence or absence of a particular edge, or of characteristics of vertices; this is valuable if knowledge of the network is not perfect. If more than one network is available, it may also be possible to compare the properties of different, but related networks, using the fitted models, and to use the comparisons to uncover scientifically interesting features. It can also be of interest to find ways of comparing whole networks with one another, when they may have very different vertex sets, but are conjectured to be related; methods discussed include the graphlet correlation distance, Netdis and NetEMD. For instance, the similarities between the protein–protein interaction networks of different species can be used as a basis for constructing phylogenies.