We review recent advances in causal inference under interference, drawing on a complex and diverse body of work ranging from causal inference, network science, the health sciences, economics, and the social sciences. Interference in connected populations implies that the treatment assignments of units can affect the outcomes of other units directly (via spillover) and indirectly (via contagion). Examples include public health interventions, economic and financial interventions, and advertising on social media. We review tests for detecting interference, causal effects based on fixed and random potential outcomes, identification of causal effects, and design- and model-based estimators of causal effects based on experimental and observational data. We then discuss the scope of causal conclusions based on fixed and random potential outcomes and interference graphs. Using simulations, we demonstrate that conditioning on interference graphs limits causal conclusions when the variability across interference graphs is high. We conclude with a selection of open problems.

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