Scenarios for the formation and evolution of hydrogen-deficient supergiants are analyzed. Some of these supergiants may possibly be identified as R CrB stars. The main scenarios involve (1) a final, post-hydrogen-burning, helium shell flash in the central star of a planetary nebula, (2) the merger of hydrogen-deficient components of evolved close binaries, and (3) the merger of a neutron star with a helium-rich star. R CrB stars produced in all scenarios are progeny of relatively low mass stars (0.8-6.0 M.) and many are among the oldest stars in our Galaxy, a result which helps explain their relatively large average distances from the Galactic plane. In the single star scenario, the nucleosynthesis and mixing required to explain observed abundances has been demonstrated explicitly by model calculations, whereas the corresponding processes in binary star scenarios must be postulated until appropriate two-dimensional or three-dimensional hydrodynamic merger models have been constructed. Birthrates, observed numbers, and other main parameters of R CrB stars and of other hydrogen-deficient stars which arise in close binaries after a merger of evolved components are estimated with a numerical scenario model which provides distributions over masses, ages, and distances from the Galactic plane. A comparison of scenario model predictions with properties of observed R CrB stars suggests that there are lower limits on the initial stellar mass and on the mass of the degenerate (CO or ONe) core of a helium star if it is to become an R CrB star. Estimates of both limits require further calculations of helium giant star models with appropriate envelope compositions and opacities adequate for these compositions. It is also clear that a stellar wind plays a decisive role in determining the number of R CrB stars produced by binary and single stars. The birthrate of R CrB stars produced by single stars and by components of wide noninteracting binary stars is estimated to be between 0.01 yr(-1) and 0.1 yr(-1), and the birthrate of those produced by mergers of components of close binary stars is estimated to be in the range similar to 0.004-0.007 yr(-1). The helium fuel initially available for binary-produced R CrB stars is typically 20 times larger than is available in R CrB stars produced by single star evolution, suggesting that most observed R CrB stars originate in close binaries. The fact that only similar to 10% of observed R CrB stars are associated with an extended nebula which is visible at optical, IR, or both wavelengths supports this inference. On the other hand, since relevant model calculations which show that merger products generate appropriate compositions do not exist, the single star scenario cannot be catagorically excluded as the major producer of R CrB stars. Mergers may be progenitors of hydrogen-deficient stars of other types. Roughly 10% of all single stars and stars in wide binaries undergo a final, post-hydrogen-burning helium flash and evolve into non-DA white dwarfs, whether or not they pass through an R CrB phase. Approximately 15% of all single stars and stars in wide binaries undergo a final helium flash before hydrogen burning ceases during the planetary nebula stage. These stars probably evolve into shell helium-burning giants and, if wind mass loss is efficient enough, they will ultimately evolve into non-DA white dwarfs. Roughly 20% of all close binaries produce single hydrogen-deficient stars which evolve into non-DA white dwarfs, whether or not they pass through an R CrB phase. White dwarfs of mass equal to or greater than 0.8 M. which descend from single stars and stars in wide binaries lose their hydrogen-rich envelope during the first 10(8) yr of the white dwarf cooling phase and also become non-DA dwarfs. Thus the theory of stellar evolution predicts that perhaps up to similar to 45% of all white dwarfs are of the non-DA variety. Those helium supergiants which are formed by way of mergers and have sufficiently massive (ONe) degenerate cores may terminate their evolution as supernovae. The frequency of such events in our Galaxy, as given by the scenario code, is similar to 6 x 10(-4) yr(-1), suggesting that perhaps one out of every 10-20 helium supergiants made by close binaries may complete its evolution as a hydrogen-free supernova.
