I will present a series of experiments aiming to define how language comprehension is modulated when a native listener is facing a non-native speaker. In the project, we explored this question regarding different fundamental aspects of sentence comprehension: syntactic, semantic and pragmatic processing. Regarding syntactic processing, we showed that the way the brain reacts to grammatical errors depends on the linguistic status of the speaker, as well as on the frequency of errors in real life. Regarding the semantic level, we showed that processing of dialectal synonyms, cognates, and semantic violations differ when listening to native and non-native speakers, and we also revealed that anticipatory processes are affected by the speaker’s accent. Finally, regarding pragmatics, we showed that ironic statements are processed differently when uttered by a native or non-native speaker. In its whole, this project provides important advances on our knowledge on sentence/discourse comprehension. The results we obtained are relevant at the pragmatic level, providing a better understanding on how native listeners manage to comprehend foreign speakers, and at the theoretical level, showing how sentence comprehension is recalibrated on-line depending on external cues such as the speaker’s accent.