Title: Iteratively Learning from the Best. Abstract: We study a simple generic framework to address the issue of bad training data; both bad labels in supervised problems, and bad samples in unsupervised ones. Our approach starts by fitting a model to the whole training dataset, but then iteratively improves it by alternating between (a) revisiting the training data to select samples with lowest current loss, and (b) re-training the model on only these selected samples. It can be applied to any existing model training setting which provides a loss measure for samples, and a way to refit on new ones. We show the merit of this approach in both theory and practice We first prove statistical consistency, and linear convergence to the ground truth and global optimum, for two simpler model settings: mixed linear regression, and gaussian mixture models.  We then demonstrate its success empirically in (a) saving the accuracy of existing deep image classifiers when there are errors in the labels of training images, and (b) improving the quality of samples generated by existing DC-GAN models, when it is given training data that contains a fraction of the images from a different and unintended dataset.  The experimental results show  significant improvement over the baseline methods that ignore the existence of bad labels/samples. 