Automatic gesture generation is a field of growing interest, and a key technology for enabling embodied conversational agents. Research into gesture generation is rapidly gravitating towards data-driven methods. Unfortunately, individual research efforts in the field are difficult to compare: there are no established benchmarks, and each study tends to use its own dataset, motion visualisation, and evaluation methodology. To address this situation, we launched the GENEA gesture-generation challenge, wherein participating teams built automatic gesture-generation systems on a common dataset, and the resulting systems were evaluated in parallel in a large, crowdsourced user study. Since differences in evaluation outcomes between systems now are solely attributable to differences between the motion-generation methods, this enables benchmarking recent approaches against one another and investigating the state of the art in the field. This paper provides a first report on the purpose, design, and results of our challenge, with each individual team's entry described in a separate paper also presented at the GENEA Workshop. Additional information about the workshop can be found at https://genea-workshop.github.io/2020/ .