This article was inspired by some works of Belyaev in which he discussed the biosocial human nature, and is dedicated to the 100 year anniversary of Belyaev' birth. The main views and theories of the human nature and the main paths of genome and culture evolution during anthropogenesis are overviewed. The views of the leading past and present world-wide scientists on the basic principles of the genome-culture interactions are discussed. The seeming contradictions between "geneticists" and "sociologists" are resolved due to the development of the concept of co-evolution of the genome and culture. The evolution of genes and culture is a whole, but not separate processes. During their evolution, humans modify and reconstruct their sociocultural environment. The new environment creates new selection vectors and forms new ways and directions for genetic evolution. In response to the culture development, the genetic determination of human cognitive processes also changed. A good example of the co-evolution of culture and the genome is the development of human speech, the voice and mimic apparatus of communication. The vital importance of the new possibilities for social communication in human populations disposes to the fixation of genetic features that facilitate such communication. At the early stages of human evolution, the areas of the cerebral cortex that were responsible for the development of speech expanded and reorganized. The point of genome-culture co-evolution is well illustrated by niche construction theory. It is emphasized that the evolution of culture, which is widely regarded as a non-biological phenomenon, is quite similar in all its respects to the Darwinian process, as a result of which a sociocultural environment that is adaptive for a given community is formed through selection and transmission in a series of generations. In fact, we are talking about epigenetic inheritance in the evolution of culture and morality. The review details the views and theoretical concepts of geneticists, sociologists, social psychologists, anthropologists, behaviorists and ethologists in explaining the phenomenon of human evolution. Some contradictions caused by different rates of evolution of culture and genome are considered. In conclusion, it is shown that Belyaev's interpretation of the biosocial nature of humans finds confirmation in modern studies by geneticists, sociologists and psychologists.