This chapter provides an introduction to task engagement as a framework for better understanding how individuals participate in and learn from second language activities in their leisure time. Although the concept is relatively new to second language acquisition research, engagement has been extensively studied in educational science, as a way of operationalising different aspects of students’ participation in learning activities (Christenson, Reschly and Wylie 2012). Engagement is most commonly defined in terms of behavioural, cognitive, and affective dimensions, referring broadly to the way in which students act, think, and feel in educational contexts (Oga- Baldwin 2019). In order to explore the nature of engagement in informal second language learning (ISLL), the current chapter reviews prior research and presents a selection of novel findings from a large-scale mixed-methods study of engagement in informal activities among students of English as a foreign language in German secondary schools (Arndt 2019). Whereas prior ISLL research focused primarily on behavioural engagement, that is, the quantity and diversity of second language activities in which learners participate in their leisure time, the current study also considered affective and cognitive engagement, or the ways in which students think and feel about informal second language activities. To increase the applicability of the engagement framework to the study of language learning (both in- and outside of the classroom), an additional linguistic engagement dimension is proposed, referring to the extent to which learners consciously focus on processing linguistic features they encounter and improving their language skills. The findings suggest that these four engagement dimensions play different roles in the informal language learning process and that they are highly complex and dynamic, in that engagement can vary between students (alongside, for example, their personal interests and L2 proficiency) and different types of informal activities (depending on the medium, linguistic difficulty, narrative complexity, etc.).