The promotive effect of auxin on shoot cell expansion provided the bioassay used to isolate this central plant hormone nearly a century ago. While the mechanisms underlying auxin perception and signaling to regulate transcription have largely been elucidated, how auxin controls cell expansion is only now attaining molecular-level definition. The good news is that the decades-old acid growth theory invoking plasma membrane H⁺-ATPase activation is still useful. The better news is that a mechanistic framework has emerged, wherein Small Auxin Up RNA (SAUR) proteins regulate protein phosphatases to control H⁺-ATPase activity. In this review, we focus on rapid auxin effects, their relationship to H⁺-ATPase activation and other transporters, and dependence on TIR1/AFB signaling. We also discuss how some observations, such as near-instantaneous effects on ion transport and root growth, do not fit into a single, comprehensive explanation of how auxin controls cell expansion, and where more research is warranted. Expected final online publication date for the Annual Review of Plant Biology, Volume 71 is April 29, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.