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We provide a perspective on the growing field of structural TCR immunoinformatics, summarizing core principles of TCR structural biology and highlighting existing resources and tools. We outline computational methods for TCR structure prediction, and discuss outstanding challenges faced by current tools, as well as potential avenues to address these. We expand on the research enabled by the availability of predicted TCR structures, exploring the utility of TCR structure predictions for computationally inferring TCR specificity, as well as summarizing opportunities emerging from the adjacent field of antibody research. 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