Learning an effective distance measurement between sample pairs plays an important role in visual analysis, where the training procedure largely relies on hard negative samples. However, hard negative samples usually account for the tiny minority in the training set, which may fail to fully describe the data distribution close to the decision boundary. In this paper, we present a deep adversarial metric learning (DAML) framework to generate synthetic hard negatives from the original negative samples, which is widely applicable to existing supervised deep metric learning algorithms. Different from existing sampling strategies which simply ignore numerous easy negatives, our DAML aim to exploit them by generating synthetic hard negatives adversarial to the learned metric as complements. We simultaneously train the feature embedding and hard negative generator in an adversarial manner, so that adequate and targeted synthetic hard negatives are created to learn more precise distance metrics. As a single transformation may not be powerful enough to describe the global input space under the attack of the hard negative generator, we further propose a deep adversarial multi-metric learning (DAMML) method by learning multiple local transformations for more complete description. We simultaneously exploit the collaborative and competitive relationships among multiple metrics, where the metrics display unity against the generator for effective distance measurement as well as compete for more training data through a metric discriminator to avoid overlapping. Extensive experimental results on five benchmark datasets show that our DAML and DAMML effectively boost the performance of existing deep metric learning approaches through adversarial learning.