Anomaly detection in medical data is often of critical importance, from diagnosing and potentially localizing disease processes such as epilepsy to detecting and preventing fatal events such as cardiac arrhythmias. Generative adversarial networks (GANs) have since their inception shown promise in various applications and have been shown to be effective in cybersecurity, data denoising, and data augmentation, and have more recently found a potentially important place in the detection of anomalies in medical time series. This chapter provides a selective review of this novel use of GANs, in the process highlighting the nature of anomalies in time series, special challenges related to medical time series, and some general issues in approaching time series anomaly detection with deep learning. We cover the most frequently applied GAN models and briefly detail the current landscape of applying GANs to anomaly detection in two commonly used medical time series, electrocardiography (ECG) and electroencephalography (EEG).