Efficient detection of multiple object instances is one of the fundamental challenges in computer vision. For certain object categories, even the best automatic systems are yet unable to produce high-quality detection results, and fully manual annotation would be an expensive process. How can detection algorithms interplay with human expert annotators? To make the best use of scarce (human) labeling resources, one needs to decide when to invoke the expert, such that the best possible performance can be achieved while requiring a minimum amount of supervision. In this paper, we propose a principled approach to active object detection, and show that for a rich class of base detectors algorithms, one can derive a natural sequential decision problem for deciding when to invoke expert supervision. We further show that the objective function satisfies adaptive submodularity, which allows us to derive strong performance guarantees for our algorithm. We demonstrate the proposed algorithm on three real-world tasks, including a problem for biodiversity monitoring from micro UAVs in the Sumatra rain forest. Our results show that active detection not only outperforms its passive counterpart; for certain tasks, it also works significantly better than straightforward application of existing active learning techniques. To the best of our knowledge, our approach is the first to rigorously address the active detection problem from both empirical and theoretical perspectives.