Instance contrast for unsupervised representation learning has achieved great success in recent years. In this work, we explore the idea of instance contrastive learning in unsupervised domain adaptation (UDA) and propose a novel Category Contrast technique (CaCo) that introduces semantic priors on top of instance discrimination for visual UDA tasks. By considering instance contrastive learning as a dictionary look-up operation, we construct a semantics-aware dictionary with samples from both source and target domains where each target sample is assigned a (pseudo) category label based on the category priors of source samples. This allows category contrastive learning (between target queries and the category-level dictionary) for category-discriminative yet domain-invariant feature representations: samples of the same category (from either source or target domain) are pulled closer while those of different categories are pushed apart simultaneously. Extensive UDA experiments in multiple visual tasks (, segmentation, classification and detection) show that the simple implementation of CaCo achieves superior performance as compared with the highly-optimized state-of-the-art methods. Analytically and empirically, the experiments also demonstrate that CaCo is complementary to existing UDA methods and generalizable to other learning setups such as semi-supervised learning, unsupervised model adaptation, etc.