Recent insights into the physical biology of plant cell walls are reviewed, summarizing the essential differences between primary and secondary cell walls and identifying crucial gaps in our knowledge of their structure and biomechanics. Unexpected parallels are identified between the mechanism of expansion of primary cell walls during growth and the mechanisms by which hydrated wood deforms under external tension. There is a particular need to revise current 'cartoons' of plant cell walls to be more consistent with data from diverse approaches and to go beyond summarizing limited aspects of cell walls, serving instead as guides for future experiments and for the application of new techniques.