With the recent advancements in generative modeling, the realism of deepfake content has been increasing at a steady pace, even reaching the point where people often fail to detect manipulated media content online, thus being deceived into various kinds of scams. In this paper, we survey deepfake generation and detection techniques, including the most recent developments in the field, such as diffusion models and Neural Radiance Fields. Our literature review covers all deepfake media types, comprising image, video, audio and multimodal (audio-visual) content. We identify various kinds of deepfakes, according to the procedure used to alter or generate the fake content. We further construct a taxonomy of deepfake generation and detection methods, illustrating the important groups of methods and the domains where these methods are applied. Next, we gather datasets used for deepfake detection and provide updated rankings of the best performing deepfake detectors on the most popular datasets. In addition, we develop a novel multimodal benchmark to evaluate deepfake detectors on out-of-distribution content. The results indicate that state-of-the-art detectors fail to generalize to deepfake content generated by unseen deepfake generators. Finally, we propose future directions to obtain robust and powerful deepfake detectors. Our project page and new benchmark are available at https://github.com/CroitoruAlin/biodeep.