We consider adversarial examples in the black-box decision-based scenario. Here, an attacker has access to the final classification of a model, but not its parameters or softmax outputs. Most attacks for this scenario are based either on transferability, which is unreliable, or random sampling, which is often slow. Focusing on the latter, we propose to improve the efficiency of sampling-based attacks with prior beliefs about the target domain. We identify two such priors, image frequency and surrogate gradients, and discuss how to integrate them into a unified sampling procedure. We then formulate the Biased Boundary Attack, which achieves a drastic speedup over the original Boundary Attack. We demonstrate the effectiveness of our approach against an ImageNet classifier. We also showcase a targeted attack for the Google Cloud Vision API, where we craft convincing examples with just a few hundred queries. Finally, we demonstrate that our approach outperforms the state of the art when facing strong defenses: Our attack scored second place in the targeted attack track of the NeurIPS 2018 Adversarial Vision Challenge.