Charles Darwin, the founder of the idea of natural selection, believed that this selection is not limited exclusively to biology: changes in language, consciousness, and technology are also adaptive. The transmission of culture is not a human prerogative. To date, several approaches for the understanding of the biological basis of cultural evolution were developed. Memetics stands out among other interdisciplinary theories that consider the development of culture and society through the prism of biological phenomena, because it is based on the concept of the biological replicator, meme and the mechanisms of cultural evolution are understood by analogy with biological evolution. The concepts of the biological and cultural replicators are similar; however, the nature of memes and the specific mechanisms of their replication are still poorly understood. In this review, we consider the strengths and weaknesses of the memetic approach to the study of cultural phenomena in the context of the cultural and technological evolution of mankind.