As machine learning systems grow in scale, so do their training data requirements, forcing practitioners to automate and outsource the curation of training data in order to achieve state-of-the-art performance. The absence of trustworthy human supervision over the data collection process exposes organizations to security vulnerabilities; training data can be manipulated to control and degrade the downstream behaviors of learned models. The goal of this work is to systematically categorize and discuss a wide range of dataset vulnerabilities and exploits, approaches for defending against these threats, and an array of open problems in this space.