The beautifully orchestrated regulation of cell shape and volume are central themes in cell biology and physiology. Though it is less well recognized, cell surface area regulation also constitutes a distinct task for cells. Maintaining an appropriate surface area is no automatic side effect of volume regulation or shape change. The issue of surface area regulation (SAR) would be moot if all cells resembled mammalian erythrocytes in being constrained to change shape and volume using existing surface membrane. But these enucleate cells are anomalies, possessing no endomembrane. Most cells use endomembrane to continually rework their plasma membrane, even while maintaining a given size or shape. This membrane traffic is intensively studied, generally with the emphasis on targeting and turnover of proteins and delivery of vesicle contents. But surface area (SA) homeostasis, including the controlled increase or decrease of SA, is another of the outcomes of trafficking. Our principal aims, then, are to highlight SAR as a discrete cellular task and to survey evidence for the idea that membrane tension is central to the task. Cells cannot directly "measure" their volume or SA, yet must regulate both. We posit that a homeostatic relationship exists between plasma membrane tension and plasma membrane area, which implies that cells detect and respond to deviations around a membrane tension set point. Maintenance of membrane strength during membrane turnover, a seldom-addressed aspect of SA dynamics, we examine in the context of SAR. SAR occurs in both animal and plant cells. The review shows the latter to be a continuing source of groundbreaking work on tension-sensitive SAR, but is principally slanted to animal cells.