We are interested in large-scale image classification and especially in the setting where images corresponding to new or existing classes are continuously added to the training set. Our goal is to devise classifiers which can incorporate such images and classes on-the-fly at (near) zero cost. We cast this problem into one of learning a metric which is shared across all classes and explore k-nearest neighbor (k-NN) and nearest class mean (NCM) classifiers. We learn metrics on the ImageNet 2010 challenge data set, which contains more than 1.2M training images of 1K classes. Surprisingly, the NCM classifier compares favorably to the more flexible k-NN classifier, and has comparable performance to linear SVMs. We also study the generalization performance, among others by using the learned metric on the ImageNet-10K dataset, and we obtain competitive performance. Finally, we explore zero-shot classification, and show how the zero-shot model can be combined very effectively with small training datasets.