Title: Explainability for fair machine learning. Abstract: As the decisions made or influenced by machine learning models increasingly impact our lives, it is crucial to detect, understand, and mitigate unfairness. But even simply determining what ``unfairness'' should mean in a given context is non-trivial: there are many competing definitions, and choosing between them often requires a deep understanding of the underlying task. It is thus tempting to use model explainability to gain insights into model fairness, however existing explainability tools do not reliably indicate whether a model is indeed fair. In this work we present a new approach to explaining fairness in machine learning, based on the Shapley value paradigm. Our fairness explanations attribute a model's overall unfairness to individual input features, even in cases where the model does not operate on sensitive attributes directly. Moreover, motivated by the linearity of Shapley explainability, we propose a meta algorithm for applying existing training-time fairness interventions, wherein one trains a perturbation to the original model, rather than a new model entirely. By explaining the original model, the perturbation, and the fair-corrected model, we gain insight into the accuracy-fairness trade-off that is being made by the intervention. We further show that this meta algorithm enjoys both flexibility and stability benefits with no loss in performance.