The current state of the problem of the breaking of mirror symmetry in the organic medium in the course of the appearance of life is reviewed. A detailed analysis of the data available leads to the conclusion that the stage in which the various components of the future biopolymers (amino acids, sugars, etc.) formed and accumulated in racemic form must have been followed by a stage of a strong breaking of mirror symmetry and a deracemization of the organic medium. The deracemization process was a cooperative, bifurcation process. Analysis shows that the sign of the chiral polarization of the biosphere (L-amino acids, D-sugars) was the result of a ``memory'' of a random selection in the course of a bifurcation, rather than a consequence of parity breaking in weak interactions. The possibilities of a breaking of mirror symmetry in the ``warm'' (terrestrial) and ``cold'' (extraterrestrial) scenarios of the origin of life are analyzed. The model of a destruction of the biosphere as a result of long-term global racemizing perturbations is also discussed.