Collecting large-scale data with clean labels for supervised training of neural networks is practically challenging. Although noisy labels are usually cheap to acquire, existing methods suffer a lot from label noise. This paper targets at the challenge of robust training at high label noise regimes. The key insight to achieve this goal is to wisely leverage a small trusted set to estimate exemplar weights and pseudo labels for noisy data in order to reuse them for supervised training. We present a holistic framework to train deep neural networks in a way that is highly invulnerable to label noise. Our method sets the new state of the art on various types of label noise and achieves leading performance on large-scale datasets with real-world label noise. For instance, on CIFAR100 with a 40% uniform noise ratio and only 10 trusted labeled data per class, our method achieves 80.2% classification accuracy, where the error rate is only 1.4% higher than a neural network trained without label noise. Moreover, increasing the noise ratio to 80%, our method still maintains a high accuracy of 75.5%, compared to the previous best accuracy 48.2%.