In the field of Micro Air Vehicle (MAV) research the use of flapping wings attracts a lot of interest. The potential of flapping wings lies in their efficiency at small scales and their large flight envelope with a single configuration. They have the possibility of performing both energy efficient long distance flights as well as hovering flights. Most studies on Flapping Wing MAVs (FWMAVs) have focused on the design of the airframe and making them able to fly. Currently, the state-of-the-art permits investigation of the necessary autonomous flight capabilities of FWMAVs. Most previous studies have made important preliminary steps by using external cameras or an onboard camera with the FWMAV flying in a modified environment. However, since autonomy is most useful for flight in unknown areas, it will be necessary to use an onboard camera while flying in unmodified environments. Research in this direction has been performed on the DelFly. In particular, the well-known cue of optic flow was found to be rather unreliable for the determination of 3D distances, and it was complemented by a novel visual appearance cue. Since the combination of these cues may still not be sufficient for robust and long-term obstacle avoidance, this study focuses on a different well-known method to extract 3D information on the environment: stereo vision. The potential advantage of stereo vision over optic flow is that it can provide instantaneous distance estimates, implying a reduced dependence on the complex camera movements during flapping flight. The goal is to employ stereo vision in a computationally efficient way in order to achieve obstacle avoidance. The focus of this study is on using heading control for this task. Four main contributions are made: The first contribution comprises an extensive study on literature in the field of computational stereo vision. This research has been done for decades and a lot of methods were developed. These mainly focus on optimizing the quality of the results, while disregarding computational complexity. In this study the focus was on finding one or more time efficient methods that give sufficient quality to perform robust obstacle avoidance. It was concluded that Semi-Global Matching is a good candidate. The second contribution is that for the first time it has been investigated what the requirements are for a stereo vision system to do successful stereo vision-based obstacle avoidance on FWMAVs. In order to achieve accurate stereo vision results, both hardware and software aspects are found to be of importance. FWMAVs can carry only a small amount of payload and therefore there is a large restriction on sensor weight. The third contribution is the development of a systematical way to use the 3D information extracted by the stereo vision algorithm in order to find a guaranteed collision-free flight path. The focus was on dealing with the limited maneuverability of the MAV and the limited view angle of the camera. The fourth contribution is in giving an indication on the usefulness of stereo vision based on multiple experiments. These focus on determining the accuracy of the obstacle detection method as well as on validating the functionality of the obstacle avoidance strategy. The designed system proved to be successful for the task of obstacle avoidance with FWMAVs. The DelFly II successfully avoided the walls in an indoor office space of 7.3×8.2m for more than 72 seconds. This is a considerable improvement over previous monocular solutions. Since even reasonable obstacle detection could be performed for low-textured white walls, the experiments clearly show the potential of stereo vision for obstacle avoidance of FWMAVs. In combination with existing methods for speed and height control the proposed system has the potential of making fully autonomous (flapping wing) MAVs possible.