The purpose of this chapter is to introduce cyber security researchers to key concepts in modern control and game theory that are relevant to Moving Target Defenses and Adaptive Cyber Defense. We begin by observing that there are fundamental differences between control models and game models that are important for security practitioners to understand. Those differences will be illustrated through simple but realistic cyber operations scenarios, especially with respect to the types and amounts of data require for modeling. In addition to modeling differences, there are a variety of ways to think about what constitutes a “solution.” Moreover, there are significant differences in the computational and information requirements to compute solutions for various types of Adaptive Cyber Defense problems. This material is presented in the context of the advances documented in this book, the various chapters of which describe advances made in the 2012 ARO ACD MURI.