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, learned meta-information helpful for training on a particular task. We present gradient-based methods to learn commentaries, leveraging recent work on implicit differentiation for scalability. We explore diverse applications of commentaries, from weighting training examples, to parameterising label-dependent data augmentation policies, to representing attention masks that highlight salient image regions. We find that commentaries can improve training speed and/or performance, and provide insights about the dataset and training process. We also observe that commentaries generalise: they can be reused when training new models to obtain performance benefits, suggesting a use-case where commentaries are stored with a dataset and leveraged in future for improved model training.