Summary: Data Envelopment Analysis (DEA) allows us to capture the complex relationship between multiple inputs and outputs in firms and organizations. Unfortunately, managers may find it hard to understand a DEA model and this may lead to mistrust in the analyses and to difficulties in deriving actionable information from the model. In this paper, we propose to use the ideas of target setting in DEA and of counterfactual analysis in Machine Learning to overcome these problems. We define DEA counterfactuals or targets as alternative combinations of inputs and outputs that are close to the original inputs and outputs of the firm and lead to desired improvements in its performance. We formulate the problem of finding counterfactuals as a bilevel optimization model. For a rich class of cost functions, reflecting the effort an inefficient firm will need to spend to change to its counterfactual, finding counterfactual explanations boils down to solving Mixed Integer Convex Quadratic Problems with linear constraints. We illustrate our approach using both a small numerical example and a real-world dataset on banking branches.