Domain adaptation (DA) enables knowledge transfer from a labeled source domain to an unlabeled target domain by reducing the cross-domain distribution discrepancy. Most prior DA approaches leverage complicated and powerful deep neural networks to improve the adaptation capacity and have shown remarkable success. However, they may have a lack of applicability to real-world situations such as real-time interaction, where low target inference latency is an essential requirement under limited computational budget. In this paper, we tackle the problem by proposing a dynamic domain adaptation (DDA) framework, which can simultaneously achieve efficient target inference in low-resource scenarios and inherit the favorable cross-domain generalization brought by DA. In contrast to static models, as a simple yet generic method, DDA can integrate various domain confusion constraints into any typical adaptive network, where multiple intermediate classifiers can be equipped to infer "easier" and "harder" target data dynamically. Moreover, we present two novel strategies to further boost the adaptation performance of multiple prediction exits: 1) a confidence score learning strategy to derive accurate target pseudo labels by fully exploring the prediction consistency of different classifiers; 2) a class-balanced self-training strategy to explicitly adapt multi-stage classifiers from source to target without losing prediction diversity. Extensive experiments on multiple benchmarks are conducted to verify that DDA can consistently improve the adaptation performance and accelerate target inference under domain shift and limited resources scenarios