All plant cells are surrounded by a cell wall that provides cohesion, protection, and a means of directional growth to plants. Cellulose microfibrils contribute the main biomechanical scaffold for most of these walls. The biosynthesis of cellulose, which typically is the most prominent constituent of the cell wall and therefore Earth's most abundant biopolymer, is finely attuned to developmental and environmental cues. Our understanding of the machinery that catalyzes and regulates cellulose biosynthesis has substantially improved due to recent technological advances in, for example, structural biology and microscopy. Here, we provide a comprehensive overview of the structure, function, and regulation of the cellulose synthesis machinery and its regulatory interactors. We aim to highlight important knowledge gaps in the field, and outline emerging approaches that promise a means to close those gaps.