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Most existing studies on unsupervised domain adaptation (UDA) assume that each domain's training samples come with domain labels (e.g., painting, photo). Samples from each domain are assumed to follow the same distribution and the domain labels are exploited to learn domain-invariant features via feature alignment. However, such an assumption often does not hold true -- there often exist numerous finer-grained domains (e.g., dozens of modern painting styles have been developed, each differing dramatically from those of the classic styles). Therefore, forcing feature distribution alignment across each artificially-defined and coarse-grained domain can be ineffective. In this paper, we address both single-source and multi-source UDA from a completely different perspective, which is to view each instance as a fine domain. Feature alignment across domains is thus redundant. Instead, we propose to perform dynamic instance domain adaptation (DIDA). Concretely, a dynamic neural network with adaptive convolutional kernels is developed to generate instance-adaptive residuals to adapt domain-agnostic deep features to each individual instance. This enables a shared classifier to be applied to both source and target domain data without relying on any domain annotation. Further, instead of imposing intricate feature alignment losses, we adopt a simple semi-supervised learning paradigm using only a cross-entropy loss for both labeled source and pseudo labeled target data. Our model, dubbed DIDA-Net, achieves state-of-the-art performance on several commonly used single-source and multi-source UDA datasets including Digits, Office-Home, DomainNet, Digit-Five, and PACS.