Purpose: This paper aims to offer practical guidance on teaching about digital extremism -- defined here as the intersection of digital disinformation campaigns with political extremism -- by highlighting four pedagogical challenges: the danger of unintentionally "redpilling" students; the slippery slope to false equivalency and "bothsidesism" in turbulent partisan waters; the difficulty of separating empirical analyses from prescriptive debates circulating in popular media; and the trouble of getting students to understand digital extremism as a sociotechnical problem rather than as a social-or-technical problem. The conclusion proposes opportunities for educators to integrate practical approaches to confronting digital extremism with digital civics curricula. Design/methodology/approach: This paper reviews pedagogical challenges and outlines a curricular program for teaching about digital extremism drawn from the author's experience designing undergraduate courses and open teaching modules between 2016 and 2021. Findings: Educators should shift focus from the substance of digital extremism to its tools -- social media platforms' surveillance and data-gathering methods, advertising technologies and monetized user-generated content, personalized recommendation algorithms and media manipulation strategies that amplify some narratives while suppressing others -- and the media and political institutions that benefit most from it. Proposed lessons include: how digital extremists manipulate social media metadata; engagement with data creation and targeting practices; and analysis of information production, circulation and consumption exploring media manipulation tools and their effects. Originality/value: This paper's added values are the insights and practical recommendations for undergraduate educators teaching on a topic of urgent contemporary concern: digital extremism.