Despite decades of intensive search for compounds that modulate the activity of particular protein targets, a large proportion of the human kinome remains as yet undrugged. Effective approaches are therefore required to map the massive space of unexplored compound-kinase interactions for novel and potent activities. Here, we carry out a crowdsourced benchmarking of predictive algorithms for kinase inhibitor potencies across multiple kinase families tested on unpublished bioactivity data. We find the top-performing predictions are based on various models, including kernel learning, gradient boosting and deep learning, and their ensemble leads to a predictive accuracy exceeding that of single-dose kinase activity assays. We design experiments based on the model predictions and identify unexpected activities even for under-studied kinases, thereby accelerating experimental mapping efforts. The open-source prediction algorithms together with the bioactivities between 95 compounds and 295 kinases provide a resource for benchmarking prediction algorithms and for extending the druggable kinome.