The current state of the theory of biological evolution is reviewed. Evolution is compared with the cosmological processes of structure formation. Both occur in dissipative systems and are governed by export of entropy. The objections to Darwin's theory are discussed and rejected. A sufficient material for evolution is indicated, as determined by the vast supply of variability of organisms. The reasons for this variability are described. The problems of speciation are discussed and its similarity to phase transitions is demonstrated. The phenomena of punctuated equilibrium and phyletic gradualism are described and examples of both are given. Special attention is paid to directional evolution. The views of L.S. Berg are examined in detail. Directionality is governed by natural selection, and also by the type of organism that has evolved and its possible variations. The link between individual and evolutionary development is studied. Wolpert's theory of positional information is presented and the concept of the model theory of morphogenesis is outlined. It is shown that a number of traits of organisms may have no adaptive value. The evolution of the visual organ is described. The molecular foundations of evolution and the neutralist theory, according to which the evolution of proteins and nucleic acids occurs to a considerable extent independently of natural selection, are studied in detail. Arguments in favor of this theory are presented and its physical meaning disclosed, which reduces to degeneracy in the correspondence between the primary structure of a protein and its biologic function. The results are presented of current studies that indicate the inconstancy of genomes, with various pathways of altering their structure and regulation. Various aspects of applications of information theory to problems of evolution are examined in detail. The evolutionary significance of the value of information, as defined as its nonredundancy, or irreplaceability, is stressed. The connection between the value of information and its complexity is studied. The value of information increases in the course of evolution. In conclusion, the sufficiency of material and time for evolution and the correctness of Darwin's theory are noted. Current problems of evolutionary theory are pointed out.