The main goal of this thesis is to bridge the gap between trajectory tracking and interaction control for flying robots in order to allow physical interaction under wind influence by making aerial robots aware of the disturbance, interaction, and faults acting on them. This is accomplished by reasoning about the external wrench (force and torque) acting on the robot, and discriminating (distinguishing) between wind, interactions, and collisions. This poses the following research questions. First, is discrimination between the external wrench components even possible in a continuous real-time fashion for control purposes? Second, given the individual wrench components, what are effective control schemes for interaction and trajectory tracking control under wind influence? Third, how can unexpected faults, such as collisions with the environment, be detected and handled efficiently and effectively? In the interest of the first question, a fourth can be posed: is it possible to obtain a measurement of the wind speed that is independent of the external wrench? In this thesis, model-based methods are applied in the pursuit of answers to these questions. This requires a good dynamics model of the robot, as well as accurately identified parameters. Therefore, a systematic parameter identification procedure for aerial robots is developed and applied. Furthermore, external wrench estimation techniques from the field of robot manipulators are extended to be suitable for aerial robots without the need of velocity measurements, which are difficult to obtain in this context. Based on the external wrench estimate, interaction control techniques (impedance and admittance control) are extended and applied to flying robots, and a thorough stability proof is provided. Similarly, the wrench estimate is applied in a geometric trajectory tracking controller to compensate external disturbances, to provide zero steady-state error under wind influence without the need of integral control action. The controllers are finally combined into a novel compensated impedance controller, to facilitate the main goal of the thesis. Collision detection is applied to flying robots, providing a low level reflex reaction that increases safety of these autonomous robots. In order to identify aerodynamic models for wind speed estimation, flight experiments in a three-dimensional wind tunnel were performed using a custom-built hexacopter. This data is used to investigate wind speed estimation using different data-driven aerodynamic models. It is shown that good performance can be obtained using relatively simple linear regression models. In this context, the propeller aerodynamic power model is used to obtain information about wind speed from available motor power measurements. Leveraging the wind tunnel data, it is shown that power can be used to obtain the wind speed. Furthermore, a novel optimization-based method that leverages the propeller aerodynamics model is developed to estimate the wind speed. Essentially, these two methods use the propellers as wind speed sensors, thereby providing an additional measurement independent of the external force. Finally, the novel topic of simultaneously discriminating between aerodynamic, interaction, and fault wrenches is opened up. This enables the implementation of novel types of controllers that are e.g. compliant to physical interaction, while compensating wind disturbances at the same time. The previously unexplored force discrimination topic has the potential to even open a new research avenue for flying robots.