Advances in computer vision as well as increasingly widespread video-based behavioral monitoring have great potential for transforming how we study animal cognition and behavior. However, there is still a fairly large gap between the exciting prospects and what can actually be achieved in practice today, especially in videos from the wild. With this perspective paper, we want to contribute towards closing this gap, by guiding behavioral scientists in what can be expected from current methods and steering computer vision researchers towards problems that are relevant to advance research in animal behavior. We start with a survey of the state-of-the-art methods for computer vision problems that are directly relevant to the video-based study of animal behavior, including object detection, multi-individual tracking, individual identification, and (inter)action recognition. We then review methods for effort-efficient learning, which is one of the biggest challenges from a practical perspective. Finally, we close with an outlook into the future of the emerging field of computer vision for animal behavior, where we argue that the field should develop approaches to unify detection, tracking, identification and (inter)action recognition in a single, video-based framework.