Abstract Irreversible cell expansion is an essential process underlying plant growth and development. Growth begins with cell wall loosening which induces wall stress relaxation which in turn generates the reduced water potential that is needed for water uptake and volumetric expansion of the cell. Most growing cell walls consist of a cellulose scaffold embedded in a matrix of polysaccharides classified as pectins and hemicelluloses. Models of the growing cell wall are tentative hypotheses about how cell wall components are linked together to make a strong yet extensible wall and have implications about the mechanism of wall expansion. Recent evidence indicates that wall loosening by expansins and specific endoglucanases may be limited to specific regions (‘biomechanical hotspots’) where cellulose microfibrils come into close contact. The growing cell wall is dynamically modified by enzymes that change the structure of pectins and hemicelluloses, thereby altering their interactions with each other and with cellulose. Growth cessation is correlated with reduced expression of genes that promote wall loosening and changes in matrix polysaccharides that lead to a less extensible cell wall. Key Concepts: Irreversible cell expansion is an essential aspect of plant growth and morphogenesis. Surface expansion of the cell wall may be highly localised, as in tip‐growing cells, or more evenly dispersed over the cell wall surface (‘diffuse growth’), occurs pattern common in most cells of the plant body. Most cells undergo a relatively brief period of rapid cell expansion after they leave the meristem and before they differentiate into mature cells. Expansive growth of plant cells requires simultaneous uptake of water into the cell and irreversible expansion of the cell wall. Cell growth begins with cell wall loosening which leads to ‘stress relaxation’ of the cell wall which in turn creates the water potential difference needed for water uptake by the cell, resulting in the physical enlargement of the cell. The growing cell wall is composed of a network of cellulose microfibrils embedded in pectins and hemicelluloses that make up the wall matrix; these materials combine to form a load‐bearing structure that controls cell mechanics and physically limits cell growth. Deposition of new polymers to the wall is usually coordinated with surface expansion, but these are separable processes. Plant cell walls enlarge more rapidly at low pH (‘acid growth’), a process that is mediated by nonenzymatic proteins named α‐expansins. Several classes of enzymes modify the structure of pectins and hemicelluloses in the cell wall, but it is not clear whether such activity modulates growth in most cases. Cessation of cell enlargement likely involves multiple processes, including tightening of the matrix‐cellulose network and reduced expression of wall‐loosening proteins.