This chapter is the core of the theoretical investigation of tethered aerial vehicles. In the first part, we provide an overview of the state of the art on the related topic. Here we highlight the drawbacks and the gaps of the proposed methods. We then define the objectives and thus the contribution of this book which aim at filling these gaps. Our complete analysis starts deriving a generic model for tethered aerial vehicles, which also includes particular instances of the system. Leveraging on this dynamic model, we investigate the differential flatness of the system, finding two different set of flat output. These reveals new and interesting properties of tethered aerial vehicles with respect to standard vehicles in contact-free flight. Exploiting this useful dynamic property, we derive two different types of controllers. One is simple to implement and suitable for quasi-static maneuvers. The other has been instead designed for the tracking of more dynamic trajectories. Finally, in order to close the control loop with real sensors, we investigate the observability of the system’s state trying to find the minimal set of sensors that makes the state observable. This analysis identifies two sensors setups, one for the 3D and one for the 2D cases. In both cases, we derive an High Gain Observe to obtain an estimation of the state from the available measurements.