Language is a quintessentially human ability. Research has long probed the functional architecture of language in the mind and brain using diverse neuroimaging, behavioral, and computational modeling approaches. However, adequate neurally-mechanistic accounts of how meaning might be extracted from language are sorely lacking. Here, we report a first step toward addressing this gap by connecting recent artificial neural networks from machine learning to human recordings during language processing. We find that the most powerful models predict neural and behavioral responses across different datasets up to noise levels. Models that perform better at predicting the next word in a sequence also better predict brain measurements—providing computationally explicit evidence that predictive processing fundamentally shapes the language comprehension mechanisms in the brain.