For decades, social researchers have argued that there is much to be learned when things go wrong.¹ In this essay, we explore what can be learned about algorithms when things do not go as anticipated, and propose the concept of algorithm trouble to capture how everyday encounters with artificial intelligence might manifest, at interfaces with users, as unexpected, failing, or wrong events. The word trouble designates a problem, but also a state of confusion and distress. We see algorithm troubles as failures, computer errors, "bugs," but also as unsettling events that may elicit, or even provoke, other perspectives on what it means to live with algorithms -- including through different ways in which these troubles are experienced, as sources of suffering, injustice, humour, or aesthetic experimentation (Meunier et al., 2019). In mapping how problems are produced, the expression algorithm trouble calls attention to what is involved in algorithms beyond computational processes.