This dissertation addresses the question, how and why do 'flying' snakes (Chrysopelea) undulate through the air? Instead of deploying paired wings or wing-like surfaces, flying snakes jump, splay their ribs into a bluff-body airfoil, and undulate through the air. Aerial undulation is the dominant feature of snake flight, but its effects on locomotor performance and stability are unknown. Chapter 2 describes a new non-equilibrium framework to analyze gliding animals and how the pitch angle affects their translational motion. Chapter 3 combines flying snake glide experiments and detailed dynamic modeling to address what is aerial undulation and how each kinematic component affects rotational stability and translational performance. Chapter 4 combines the kinematic data of Chapter 3, with elements of the non-equilibrium framework of Chapter 2, to examine the kinematics of snake flight in greater detail. This chapter also tests if our current understanding of flying snake aerodynamics is sufficient to explain the observed center of mass motion.