Plants shape their organs with a precision demanded by optimal function; organ shaping requires control over cell wall expansion anisotropy. Focusing on multicellular organs, I survey the occurrence of expansion anisotropy and discuss its causes and proposed controls. Expansion anisotropy of a unit area of cell wall is characterized by the direction and degree of anisotropy. The direction of maximal expansion rate is usually regulated by the direction of net alignment among cellulose microfibrils, which overcomes the prevailing stress anisotropy. In some stems, the directionality of expansion of epidermal cells is controlled by that of the inner tissue. The degree of anisotropy can vary widely as a function of position and of treatment. The degree of anisotropy is probably controlled by factors in addition to the direction of microfibril alignment. I hypothesize that rates of expansion in maximal and minimal directions are regulated by distinct molecular mechanisms that regulate interactions between matrix and microfibrils.