Kite energy systems are an emerging renewable energy technology. Unlike conventional turbines, kite energy systems extract wind power using tethered kites which can move freely in the wind or underwater in an ocean current. Due to the mobility, kite power systems can harvest power from regions with higher and steadier power density by moving in high-speed cross flow motion. An airborne kite energy system harnesses wind power at an altitude higher than the conventional wind turbines, while an undersea kite energy system extracts power close to the ocean surface. In this dissertation, the physical limitation, mathematical modeling, and control system design of the kite energy systems are studied. First, three major physical effects that are acting on the kite energy systems are investigated, including potential force, steady aero-/hydro-dynamic force and added mass effects. Furthermore, the dissipativity of the steady aero-/hydro-dynamic forces with respect to the apparent velocity is established. Based on this analysis, the power generation limit of the kite energy systems is studied. A power limit formulation is given which generalize the two-dimensional result to three-dimensional case. The different physical phenomenon is modeled in different coordinate systems, the difference of the density, viscosity between air and water are significant, and the kite energy system can operate in two distinct modes. To combine different physical effects into a single simulation framework, the equivalences of the kite model in different coordinate systems are established through kinematic analysis. Using these equivalent relations, a unified simulation model for airborne and undersea kite energy systems are derived. The control system design of kite energy systems is also investigated. The resulting equations of motion of kite energy systems are highly nonlinear. Therefore, Lyapunov methods are used to analyze the system behavior. Three different techniques are reviewed, including Lyapunov analysis for autonomous and non-autonomous systems, the ultimate boundedness and input-to-state stability and passivity methods. For the fixed tether length kite energy systems, the ultimate boundedness of the kite translation is established through the dissipativity of the steady aero-/hydro-dynamic force. For the variable tether length kite energy system, the input-to-state analysis is used to design the tether tension that guaranteed the boundedness of the kite translation. In both cases, the Lyapunov based methods are used to design kite rotational control systems which result in PD type control signals. Although this control scheme generates consecutive power cycles for kite energy systems. It is shown that the kite aero-/hydro-dynamical performance is unstable in the simulation which could result in unsteady power generation. To provide a steadier performance in kite translation and power output, the relative dynamics of the kite translation is first proposed. In this model, the kite apparent speed and attitudes, the angle of attack and side-slip angle, are used to describe the kite translation. A nonlinear control scheme is designed to regulate the angle of attack and side-slip angle using back-stepping methods by using the kite angular velocity and control inputs. However, due to the magnitude limit of the angular velocity, the residual error of the apparent attitude tracking remain large for the large desired angle of attack and side-slip angle. To achieve a better power harvesting and aero-/hydro-dynamics performance, the geometric properties of kite angle of attack and side-slip angle are studied. A geometric attitudes trajectory is constructed to track given apparent attitudes. A rotational control system is designed based on the back-stepping and sliding mode methods for the desired geometric attitude, and the high gain observer is applied to acquire the information needed for the rotational control signal. Through the geometric apparent attitudes tracking control algorithm, the angle of attack and side-slip angle act as direct control inputs to the kite translational motion. The kite translational dynamics under the geometric apparent attitude tracking is studied. These dynamics give the possibility of controlling the kite translational motion only through the rotational control scheme.