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In the last few years, we have witnessed a renewed and fast-growing interest in continual learning with deep neural networks with the shared objective of making current AI systems more adaptive, efficient and autonomous. However, despite the significant and undoubted progress of the field in addressing the issue of catastrophic forgetting, benchmarking different continual learning approaches is a difficult task by itself. In fact, given the proliferation of different settings, training and evaluation protocols, metrics and nomenclature, it is often tricky to properly characterize a continual learning algorithm, relate it to other solutions and gauge its real-world applicability. The first Continual Learning in Computer Vision challenge held at CVPR in 2020 has been one of the first opportunities to evaluate different continual learning algorithms on a common hardware with a large set of shared evaluation metrics and 3 different settings based on the realistic CORe50 video benchmark. In this paper, we report the main results of the competition, which counted more than 79 teams registered, 11 finalists and 2300$ in prizes. We also summarize the winning approaches, current challenges and future research directions.