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Self-attention based models such as vision transformers (ViTs) have emerged as a very competitive architecture alternative to convolutional neural networks (CNNs) in computer vision. Despite increasingly stronger variants with ever-higher recognition accuracies, due to the quadratic complexity of self-attention, existing ViTs are typically demanding in computation and model size. Although several successful design choices (e.g., the convolutions and hierarchical multi-stage structure) of prior CNNs have been reintroduced into recent ViTs, they are still not sufficient to meet the limited resource requirements of mobile devices. This motivates a very recent attempt to develop light ViTs based on the state-of-the-art MobileNet-v2, but still leaves a performance gap behind. In this work, pushing further along this under-studied direction we introduce EdgeViTs, a new family of light-weight ViTs that, for the first time, enable attention-based vision models to compete with the best light-weight CNNs in the tradeoff between accuracy and on-device efficiency. This is realized by introducing a highly cost-effective local-global-local (LGL) information exchange bottleneck based on optimal integration of self-attention and convolutions. For device-dedicated evaluation, rather than relying on inaccurate proxies like the number of FLOPs or parameters, we adopt a practical approach of focusing directly on on-device latency and, for the first time, energy efficiency. Specifically, we show that our models are Pareto-optimal when both accuracy-latency and accuracy-energy trade-offs are considered, achieving strict dominance over other ViTs in almost all cases and competing with the most efficient CNNs. Code is available at https://github.com/saic-fi/edgevit.