A brain-computer interface that decodes continuous language from non-invasive recordings would have many scientific and practical applications. Currently, however, decoders that reconstruct continuous language use invasive recordings from surgically implanted electrodes1–3, while decoders that use non-invasive recordings can only identify stimuli from among a small set of letters, words, or phrases4–7. Here we introduce a non-invasive decoder that reconstructs continuous natural language from cortical representations of semantic meaning8 recorded using functional magnetic resonance imaging (fMRI). Given novel brain recordings, this decoder generates intelligible word sequences that recover the meaning of perceived speech, imagined speech, and even silent videos, demonstrating that a single language decoder can be applied to a range of semantic tasks. To study how language is represented across the brain, we tested the decoder on different cortical networks, and found that natural language can be separately decoded from multiple cortical networks in each hemisphere. As brain-computer interfaces should respect mental privacy9, we tested whether successful decoding requires subject cooperation, and found that subject cooperation is required both to train and to apply the decoder. Our study demonstrates that continuous language can be decoded from non-invasive brain recordings, enabling future multipurpose brain-computer interfaces.