Advances in machine learning (ML) in recent years have enabled a dizzying array of applications such as data analytics, autonomous systems, and security diagnostics. ML is now pervasive - new systems and models are being deployed in every domain imaginable, leading to widespread deployment of software based inference and decision making. There is growing recognition that ML exposes new vulnerabilities in software systems, yet the technical community's understanding of the nature and extent of these vulnerabilities remains limited. We systematize findings on ML security and privacy, focusing on attacks identified on these systems and defenses crafted to date.We articulate a comprehensive threat model for ML, and categorize attacks and defenses within an adversarial framework. Key insights resulting from works both in the ML and security communities are identified and the effectiveness of approaches are related to structural elements of ML algorithms and the data used to train them. In particular, it is apparent that constructing a theoretical understanding of the sensitivity of modern ML algorithms to the data they analyze, à la PAC theory, will foster a science of security and privacy in ML.