Understanding language requires readers and listeners to cull meaning from fast-unfolding messages that often contain conflicting cues pointing to incompatible ways of interpreting the input (e.g., "The cat was chased by the mouse"). This article reviews mounting evidence from multiple methods demonstrating that cognitive control plays an essential role in resolving conflict during language comprehension. How does cognitive control accomplish this task? Psycholinguistic proposals have conspicuously failed to address this question. We introduce an account in which cognitive control aids language processing when cues conflict by sending top-down biasing signals that strengthen the interpretation supported by the most reliable evidence available. We also provide a computationally plausible model that solves the critical problem of how cognitive control "knows" which way to direct its biasing signal by allowing linguistic knowledge itself to issue crucial guidance. Such a mental architecture can explain a range of experimental findings, including how moment-to-moment shifts in cognitive-control state--its level of activity within a person--directly impact how quickly and successfully language comprehension is achieved.