Although current deep learning-based face forgery detectors achieve impressive performance in constrained scenarios, they are vulnerable to samples created by unseen manipulation methods. Some recent works show improvements in generalization but rely on cues that are easily corrupted by common post-processing operations such as compression. In this paper, we propose LipForensics, a detection approach capable of both generalizing to novel manipulations and withstanding various distortions. LipForensics targets high-level semantic irregularities in mouth movements, which are common in many generated videos. It consists in first pretraining a spatio-temporal network to perform visual speech recognition (lipreading), thus learning rich internal representations related to natural mouth motion. A temporal network is subsequently finetuned on fixed mouth embeddings of real and forged data in order to detect fake videos based on mouth movements without overfitting to low-level, manipulation-specific artifacts. Extensive experiments show that this simple approach significantly surpasses the state-of-the-art in terms of generalization to unseen manipulations and robustness to perturbations, as well as shed light on the factors responsible for its performance.