Predictive models of student success in Massive Open Online Courses (MOOCs) are a critical component of effective content personalization and adaptive interventions. In this article we review the state of the art in predictive models of student success in MOOCs and present a categorization of MOOC research according to the predictors (features), prediction (outcomes), and underlying theoretical model. We critically survey work across each category, providing data on the raw data source, feature engineering, statistical model, evaluation method, prediction architecture, and other aspects of these experiments. Such a review is particularly useful given the rapid expansion of predictive modeling research in MOOCs since the emergence of major MOOC platforms in 2012. This survey reveals several key methodological gaps, which include extensive filtering of experimental subpopulations, ineffective student model evaluation, and the use of experimental data which would be unavailable for real-world student success prediction and intervention, which is the ultimate goal of such models. Finally, we highlight opportunities for future research, which include temporal modeling, research bridging predictive and explanatory student models, work which contributes to learning theory, and evaluating long-term learner success in MOOCs.