We present Phenaki, a model capable of realistic video synthesis given a sequence of textual prompts. Generating videos from text is particularly challenging due to the computational cost, limited quantities of high quality text-video data and variable length of videos. To address these issues, we introduce a new causal model for learning video representation which compresses the video to a small discrete tokens representation. This tokenizer is auto-regressive in time, which allows it to work with video representations of different length. To generate video tokens from text we are using a bidirectional masked transformer conditioned on pre-computed text tokens. The generated video tokens are subsequently de-tokenized to create the actual video. To address data issues, we demonstrate how joint training on a large corpus of image-text pairs as well as a smaller number of video-text examples can result in generalization beyond what is available in the video datasets. Compared to the previous video generation methods, Phenaki can generate arbitrary long videos conditioned on a sequence of prompts (i.e. time variable text or story) in open domain. To the best of our knowledge, this is the first time a paper studies generating videos from time variable prompts.