We present the first neural video compression method based on generative adversarial networks (GANs). Our approach significantly outperforms previous neural and non-neural video compression methods in a user study, setting a new state-of-the-art in visual quality for neural methods. We show that the GAN loss is crucial to obtain this high visual quality. Two components make the GAN loss effective: we i) synthesize detail by conditioning the generator on a latent extracted from the warped previous reconstruction to then ii) propagate this detail with high-quality flow. We find that user studies are required to compare methods, i.e., none of our quantitative metrics were able to predict all studies. We present the network design choices in detail, and ablate them with user studies.