Binary keypoint descriptors provide an efficient alternative to their floating-point competitors as they enable faster processing while requiring less memory. In this paper, we propose a novel framework to learn an extremely compact binary descriptor we call BinBoost that is very robust to illumination and viewpoint changes. Each bit of our descriptor is computed with a boosted binary hash function, and we show how to efficiently optimize the different hash functions so that they complement each other, which is key to compactness and robustness. The hash functions rely on weak learners that are applied directly to the image patches, which frees us from any intermediate representation and lets us automatically learn the image gradient pooling configuration of the final descriptor. Our resulting descriptor significantly outperforms the state-of-the-art binary descriptors and performs similarly to the best floating-point descriptors at a fraction of the matching time and memory footprint.