Previous adversarial domain alignment methods for unsupervised domain adaptation (UDA) pursue conditional domain alignment via intermediate pseudo labels. However, these pseudo labels are generated by independent instances without considering the global data structure and tend to be noisy, making them unreliable for adversarial domain adaptation. Compared with pseudo labels, prototypes are more reliable to represent the data structure resistant to the domain shift since they are summarized over all the relevant instances. In this work, we attempt to calibrate the noisy pseudo labels with prototypes. Specifically, we first obtain a reliable prototypical representation for each instance by multiplying the soft instance predictions with the global prototypes. Based on the prototypical representation, we propose a novel Prototypical Adversarial Learning (PAL) scheme and exploit it to align both feature representations and intermediate prototypes across domains. Besides, with the intermediate prototypes as a proxy, we further minimize the intra-class variance in the target domain to adaptively improve the pseudo labels. Integrating the three objectives, we develop an unified framework termed PrototypicAl uNsupervised Domain Adaptation (PANDA) for UDA. Experiments show that PANDA achieves state-of-the-art or competitive results on multiple UDA benchmarks including both object recognition and semantic segmentation tasks.