We collect data on the masses, radii, etc., of three classes of close binary stars: low-temperature contact binaries (LTCBs), near-contact binaries (NCBs), and detached close binaries (DCBs). We restrict ourselves to systems in which (1) both components are, at least arguably, near the main sequence, (2) the periods are less than a day, and (3) there is both spectroscopic and photometric analysis leading to reasonably reliable data. We discuss the possible evolutionary connections between these three classes, emphasizing the roles played by mass loss and angular momentum loss in rapidly rotating cool stars. We describe a new mechanism, differential rotation as observed in the Sun, which can explain the remarkable efficiency of heat transport in the outer envelopes of contact binaries.