This paper presents the results and analyses stemming from the first VoicePrivacy 2020 Challenge which focuses on developing anonymization solutions for speech technology. We provide a systematic overview of the challenge design with an analysis of submitted systems and evaluation results. In particular, we describe the voice anonymization task and datasets used for system development and evaluation. Also, we present different attack models and the associated objective and subjective evaluation metrics. We introduce two anonymization baselines and provide a summary description of the anonymization systems developed by the challenge participants. We report objective and subjective evaluation results for baseline and submitted systems. In addition, we present experimental results for alternative privacy metrics and attack models developed as a part of the post-evaluation analysis. Finally, we summarize our insights and observations that will influence the design of the next VoicePrivacy challenge edition and some directions for future voice anonymization research.