We review the growing body of research on the challenging topic of interference in causal inference. Interference arises when the treatment assignments of connected units affect the outcomes of other units directly (via spillover) or indirectly (via contagion). Examples include public health, economic, political, or educational interventions, as well as advertising on social media. Adapting the Neyman-Rubin potential outcome framework, we review selected causal effects under interference and discuss identification of causal effects based on experimental and observational data. We then review statistical tests for interference and causal effects, design- and model-based estimators for causal effects, and methodological challenges, including variance reduction, unknown interference graphs, and misspecified exposure mappings. We conclude with a discussion of the scope of causal conclusions based on fixed and random potential outcomes and interference graphs. While the fixed potential outcome framework is sufficient in many applications, the random potential outcome framework can be useful when the data fall short. Examples include causal inference for heterogeneous treatment effects and external validity, including generalizability and transportability.

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