Listeners can successfully interpret the intended meaning of an utterance even when it contains errors or other unexpected anomalies. The present work combines an online measure of attention to sentence referents (visual world eye-tracking) with offline judgments of sentence meaning to disclose how the interpretation of anomalous sentences unfolds over time in order to explore mechanisms of non-literal processing. We use a metalinguistic judgment in Experiment 1 and an elicited imitation task in Experiment 2. In both experiments, we focus on one morphosyntactic anomaly (Subject-verb agreement; The key to the cabinets literally *were … ) and one semantic anomaly (Without; Lulu went to the gym without her hat ?off) and show that non-literal referents to each are considered upon hearing the anomalous region of the sentence. This shows that listeners understand anomalies by overwriting or adding to an initial interpretation and that this occurs incrementally and adaptively as the sentence unfolds.