The introduction outlines the problems involved in coming to grips with data in the form of a network. A complete pictorial description is possible only for very small networks. More commonly, it is necessary to describe a network in other ways, by choosing appropriate summary statistics, and by comparing it to other, better-understood networks. In many cases, the entire network may be unknown and may change over time, so that only network samples are available for analysis. Problems of interest include conducting statistical analyses when observations are taken from individuals linked by a network, finding communities within a network, estimating how fast an epidemic on a network may be transmitted; and judging to what extent the specification of a network may be in error.