Plant cells build nanofibrillar walls that are central to plant growth, morphogenesis and mechanics. Starting from simple sugars, three groups of polysaccharides, namely, cellulose, hemicelluloses and pectins, with very different physical properties are assembled by the cell to make a strong yet extensible wall. This Review describes the physics of wall growth and its regulation by cellular processes such as cellulose production by cellulose synthase, modulation of wall pH by plasma membrane H -ATPase, wall loosening by expansin and signalling by plant hormones such as auxin and brassinosteroid. In addition, this Review discusses the nuanced roles, properties and interactions of cellulose, matrix polysaccharides and cell wall proteins and describes how wall stress and wall loosening cooperatively result in cell wall growth.