Trying to anticipate what will happen next, or 'thinking ahead', is normal human behavior. The role of anticipation, or prediction, in language processing has been a topic of central interest in modern-day psycholinguistics. The recognition that prediction plays an important, perhaps a fundamental, role in human cognition in general, and in language processing in particular, has transformed the field of psycholinguistics over the past decades, shifting the focus from comprehension as a result of incremental integration of bottom-up information, to comprehension as a proactive mechanism driven in large part by top-down expectations (Ferreira & Chantavarin, 2018; Pickering & Gambi, 2018). It is only relatively recently that this perspective has been extended to the processing of non-native languages (Kaan, 2014; Grüter, Rohde, & Schafer, 2014, 2017), raising the question: To what extent do non-native speakers engage in predictive processing when reading or listening in their second language? I will address this question by reviewing what we know so far about the role of prediction in L2 processing and learning, and present new findings from recent and on-going studies in our lab using various experimental methodologies, including visual-world eye-tracking, written sentence continuation, and structural priming (Kim & Grüter, 2019; Kim & Grüter, under review; Grüter, Lau, & Ling, 2020; Grüter, Zhu, & Jackson, in preparation).