Automated detection of tumour lesions on positron emission tomography–computed tomography (PET/CT) image data is a clinically relevant but highly challenging task. Progress in this field has been hampered in the past owing to the lack of publicly available annotated data and limited availability of platforms for inter-institutional collaboration. Here we describe the results of the autoPET challenge, a biomedical image analysis challenge aimed to motivate research in the field of automated PET/CT image analysis. The challenge task was the automated segmentation of metabolically active tumour lesions on whole-body ¹⁸F-fluorodeoxyglucose PET/CT. Challenge participants had access to a large publicly available annotated PET/CT dataset for algorithm training. All algorithms submitted to the final challenge phase were based on deep learning methods, mostly using three-dimensional U-Net architectures. Submitted algorithms were evaluated on a private test set composed of 150 PET/CT studies from two institutions. An ensemble model of the highest-ranking algorithms achieved favourable performance compared with individual algorithms. Algorithm performance was dependent on the quality and quantity of data and on algorithm design choices, such as tailored post-processing of predicted segmentations. Future iterations of this challenge will focus on generalization and clinical translation.