Title: ACAT: Adversarial Counterfactual Attention for Classification and Detection in Medical Imaging. Abstract: In some medical imaging tasks and other settings where only small parts of the image are informative for the classification task, traditional CNNs can sometimes struggle to generalise. Manually annotated Regions of Interest (ROI) are sometimes used to isolate the most informative parts of the image. However, these are expensive to collect and may vary significantly across annotators. To overcome these issues, we propose a method to generate saliency maps, obtained from adversarially generated counterfactual images. With this method, we are able to isolate the area of interest in brain and lung CT scans without using any manual annotations. Our saliency maps, in the task of localising the lesion location out of 6 possible regions, obtain a score of $65.05 \%$ on brain CT scans, improving the score of $61.29 \%$ obtained with the best competing method. We also employ the saliency maps in a framework that refines a classifier pipeline. In particular, the saliency maps are used to obtain soft spatial attention masks that modulate the image features at different scales. We refer to our method as \emph{Adversarial Counterfactual Attention} (ACAT). ACAT increases the baseline classification accuracy of lesions in brain CT scans from $71.39 \%$ to $72.55 \%$ and of COVID-19 related findings in lung CT scans from $67.71 \%$ to $70.84 \%$ and exceeds the performance of competing methods.