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In this paper we review the rapidly emerging literature for counterfactual inference using deep neural networks. Supervised deep learning has yet to see wide spread usage in the social sciences because of the black-box nature of these algorithms. However, deep learning under potential outcomes has the potential to provide substantively interpretable models that can accommodate hundreds of covariates, allow for the precise estimation of heterogeneous treatment effects, and can tap unexplored text, image, and network data for both causal and non-causal inference. Here we provide brief primers on both deep learning and causal inference from the perspectives of Potential Outcomes and Structural Causal Models/Graphs. We thoroughly review existing approaches to balancing and inverse propensity weighting in the machine learning literature, and describe deep learning techniques like adversarial training to improve estimation. We include example implementations for some prototypical algorithms in Tensorflow2. Ideally, this paper will be of service to both social scientists interested in relevant applications of deep learning, as well as computer scientists interested in moving beyond prediction to causal inference.