Online metric learning has been widely exploited for large-scale data classification due to the low computational cost. However, amongst online practical scenarios where the features are evolving (e.g., some features are vanished and some new features are augmented), most metric learning models cannot be successfully applied to these scenarios, although they can tackle the evolving instances efficiently. To address the challenge, we develop a new online Evolving Metric Learning (EML) model for incremental and decremental features, which can handle the instance and feature evolutions simultaneously by incorporating with a smoothed Wasserstein metric distance. Specifically, our model contains two essential stages: a Transforming stage (T-stage) and a Inheriting stage (I-stage). For the T-stage, we propose to extract important information from vanished features while neglecting non-informative knowledge, and forward it into survived features by transforming them into a low-rank discriminative metric space. It further explores the intrinsic low-rank structure of heterogeneous samples to reduce the computation and memory burden especially for highly-dimensional large-scale data. For the I-stage, we inherit the metric performance of survived features from the T-stage and then expand to include the new augmented features. Moreover, a smoothed Wasserstein distance is utilized to characterize the similarity relationships among the heterogeneous and complex samples, since the evolving features are not strictly aligned in the different stages. In addition to tackling the challenges in one-shot case, we also extend our model into multishot scenario. After deriving an efficient optimization strategy for both T-stage and I-stage, extensive experiments on several datasets verify the superior performance of our EML model.