Effective training of deep neural networks can be challenging, and there remain many open questions on how to best learn these models. Recently developed methods to improve neural network training examine teaching: providing learned information during the training process to improve downstream model performance. In this paper, we take steps towards extending the scope of teaching. We propose a flexible teaching framework using commentaries, meta-learned information helpful for training on a particular task or dataset. We present an efficient and scalable gradient-based method to learn commentaries, leveraging recent work on implicit differentiation. We explore diverse applications of commentaries, from learning weights for individual training examples, to parameterizing label-dependent data augmentation policies, to representing attention masks that highlight salient image regions. In these settings, we find that commentaries can improve training speed and/or performance and also provide fundamental insights about the dataset and training process.