Many attempts have been made to define nature of viruses and to uncover their origin. Our aim within this work was to show that there are different perceptions of viruses and many concepts to explain their emergence: the virus-first concept (also called co-evolution), the escape and the reduction theories. Moreover, a relatively new concept of polyphyletic virus origin called "three RNA cells, three DNA viruses" proposed by Forterre is described herein. In this paper, not only is each thesis supported by a body of evidence but also counter-argued in the light of various findings to give more insightful considerations to the readers. As the origin of viruses and that of living cells are most probably interdependent, we decided to reveal ideas concerning nature of cellular last universal common ancestor (LUCA). Furthermore, we discuss monophyletic ancestry of cellular domains and their relationships at the molecular level of membrane lipids and replication strategies of these three types of cells. In this review, we also present the emergence of DNA viruses requiring an evolutionary transition from RNA to DNA and recently discovered giant DNA viruses possibly involved in eukaryogenesis. In the course of evolution viruses emerged many times. They have always played a key role through horizontal gene transfer in evolutionary events and in formation of the tree of life or netlike routes of evolution providing a great deal of genetic diversity. In our opinion, future findings are crucial to better understand past relations between viruses and cells and the origin of both.