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Unsupervised Domain Adaptation (UDA) aims to classify unlabeled target domain by transferring knowledge from labeled source domain with domain shift. Most of the existing UDA methods try to mitigate the adverse impact induced by the shift via reducing domain discrepancy. However, such approaches easily suffer a notorious mode collapse issue due to the lack of labels in target domain. Naturally, one of the effective ways to mitigate this issue is to reliably estimate the pseudo labels for target domain, which itself is hard. To overcome this, we propose a novel UDA method named Progressive Adaptation of Subspaces approach (PAS) in which we utilize such an intuition that appears much reasonable to gradually obtain reliable pseudo labels. Speci fically, we progressively and steadily refine the shared subspaces as bridge of knowledge transfer by adaptively anchoring/selecting and leveraging those target samples with reliable pseudo labels. Subsequently, the refined subspaces can in turn provide more reliable pseudo-labels of the target domain, making the mode collapse highly mitigated. Our thorough evaluation demonstrates that PAS is not only effective for common UDA, but also outperforms the state-of-the arts for more challenging Partial Domain Adaptation (PDA) situation, where the source label set subsumes the target one.