Fueled by recent advances in statistical modeling and the rapid growth of network data, social network analysis has become increasingly popular in sociology and related disciplines. However, a significant amount of work in the field has been descriptive and correlational, which prevents the findings from being more rigorously translated into practices and policies. This article provides a review of the popular models and methods for causal network analysis, with a focus on causal inference threats (such as measurement error, missing data, network endogeneity, contextual confounding, simultaneity, and collinearity) and potential solutions (such as instrumental variables, specialized experiments, and leveraging longitudinal data). It covers major models and methods for both network formation and network effects and for both sociocentric networks and egocentric networks. Lastly, this review also discusses future directions for causal network analysis. Expected final online publication date for the Annual Review of Sociology, Volume 48 is July 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.