Low-quality and misleading information online can hijack people’s attention, often by evoking curiosity, outrage, or anger. Resisting certain types of information and actors online requires people to adopt new mental habits that help them avoid being tempted by attention-grabbing and potentially harmful content. We argue that digital information literacy must include the competence of critical ignoring—choosing what to ignore and where to invest one’s limited attentional capacities. We review three types of cognitive strategies for implementing critical ignoring: self-nudging, in which one ignores temptations by removing them from one’s digital environments; lateral reading, in which one vets information by leaving the source and verifying its credibility elsewhere online; and the do-not-feed-the-trolls heuristic, which advises one to not reward malicious actors with attention. We argue that these strategies implementing critical ignoring should be part of school curricula on digital information literacy. Teaching the competence of critical ignoring requires a paradigm shift in educators’ thinking, from a sole focus on the power and promise of paying close attention to an additional emphasis on the power of ignoring. Encouraging students and other online users to embrace critical ignoring can empower them to shield themselves from the excesses, traps, and information disorders of today’s attention economy.