Stars exist by virtue of a stable balance between the forces of gravity and pressure. Of all the conceivable stars which might be represented by points on the mass-radius plane, only those occurring in four relatively small islands of stability arc known (or thought) to exist. The corresponding objects are supported by the pressure provided by the motions of four kinds of particles. Cold nucleon pressure allows neutron stars (d Wheeler 1966), cold electron pressure allows degenerate dwarfs, the subject of the present re view, thermal ion and electron pressure supports the ordinary stars, and photon radiation pressure the supermassive stars (d Wagoner 1969). While the radius increases by ,102 from class to class, the typical mass in each is land (excepting supermassive star.s which may not exist) is near one solar mass. Thus ordinary (,1 M0) stars can pass to either of the two condensed states without losing their identity, and their real (vs possible) existence might have been anticipated. Neutron stars were predicted in just this way, but degenerate dwarfs were discovered before our knowledge of physics was advanced enough to understand them. The original explanation (Chandrasekhar 1931a, b, 1935) of these very common stars has withstood the test of time. From the observed radii (,1O-2R0) and masses (�1M0)' the internal pressure (,CM2/R4) greatly exceeds that available from thermal motions (for Tint.rior < 10s.o0K). How ever, the number density of electrons no is so high that the zero-point momen tum (P. ' tm.l/3) provides enough pressure to support the stars at radii in the observed range. So long as the electron velocities are nonrelativistic, the degenerate pressure Pe Pe2neme-l depends on the density to the (5/3) power or on Mo/3R-5. Comparing this with the pressure required to support the star against self-gravitation ( oc M2R-4) we see that degenerate dwarfs supported by nonrelativistic electron motions have a mass-radius relation of the form Roc M-l/3. For sufficiently high mass, the electrons become relativistic, and the electron pressure Pe p.em. depends on the density to the (4/3) power or on M4/3R-4; it is no longer certain that a small enough radius can be found to bring the pressure and gravitational forces in balance. The maximum mass allowed for a spherical star-the Chandrasekhar mass limit-can b( seen