Multi-view clustering aims to partition data collected from diverse sources based on the assumption that all views are complete. However, such prior assumption is hardly satisfied in many real-world applications, resulting in the incomplete multi-view learning problem. The existing attempts on this problem still have the following limitations: 1) the underlying semantic information of the missing views is commonly ignored; 2) The local structure of data is not well explored; 3) The importance of different views is not effectively evaluated. To address these issues, this paper proposes a Unified Embedding Alignment Framework (UEAF) for robust incomplete multi-view clustering. In particular, a locality-preserved reconstruction term is introduced to infer the missing views such that all views can be naturally aligned. A consensus graph is adaptively learned and embedded via the reverse graph regularization to guarantee the common local structure of multiple views and in turn can further align the incomplete views and inferred views. Moreover, an adaptive weighting strategy is designed to capture the importance of different views. Extensive experimental results show that the proposed method can significantly improve the clustering performance in comparison with some state-of-the-art methods.