Domain adaptation improves a target task by knowledge transfer from a source domain with rich annotations. It is not uncommon that “source-domain engineering” becomes a cumbersome process in domain adaptation: the high-quality source domains highly related to the target domain are hardly available. Thus, weakly-supervised domain adaptation has been introduced to address this difficulty, where we can tolerate the source domain with noises in labels, features, or both. As such, for a particular target task, we simply collect the source domain with coarse labeling or corrupted data. In this paper, we try to address two entangled challenges of weaklysupervised domain adaptation: sample noises of the source domain and distribution shift across domains. To disentangle these challenges, a Transferable Curriculum Learning (TCL) approach is proposed to train the deep networks, guided by a transferable curriculum informing which of the source examples are noiseless and transferable. The approach enhances positive transfer from clean source examples to the target and mitigates negative transfer of noisy source examples. A thorough evaluation shows that our approach significantly outperforms the state-of-the-art on weakly-supervised domain adaptation tasks.