Network data involving three roles (e.g., sender, receiver, and target or perceiver) can be represented as a three-dimensional array. Such three-way networks arise naturally in social science research, but their analysis poses challenges. Although substantive questions often involve social mechanisms driving network change, no longitudinal methods for three-way networks currently exist. Moreover, data collection on three-way networks places a heavy burden on respondents, so sometimes only partial information is available. This talk presents two methodological contributions that start to address these limitations: a longitudinal model for fully observed three-way network data, and an inferential framework that uses two-way network data to learn about three-way relations. I will illustrate through applications what new empirical questions these methods enable us to address.