Cellulose microfibrils are a key component of plant cell walls, which in turn compose most of our renewable biomaterials. Consequently, there is considerable interest in understanding how cellulose microfibrils are made in living cells by the plant cellulose synthesis complex (CSC). This remarkable multi-subunit complex contains cellulose synthase (CESA) proteins, and it is often called a rosette due to its six-lobed shape. Each CSC moves within the plasma membrane as it spins a strong cellulose microfibril in its wake. To accomplish this biological manufacturing process, the CESAs harvest an activated sugar substrate from the cytoplasm for use in the polymerization of glucan chains. An elongating glucan is simultaneously translocated across the plasma membrane by each CESA, where the group of chains emanating from one CSC co-crystallizes into a cellulose microfibril that becomes part of the assembling cell wall. Here we review major advances in understanding CESA and CSC structure/function relationships since 2013, when ground-breaking insights about the structure of cellulose synthases in bacteria and plants were published. We additionally discuss: (a) the relationship of CSC substructure to the size of the fundamental cellulose fibril; (b) an evolutionary perspective on the driving force behind the existence of hetero-oligomeric CSCs that currently appear to dominate in land plants; and (c) how cellulose properties may be regulated by CESA and CSC activity. We also pose major questions that still remain in this rapidly changing and exciting research field.