Gene duplication plays a pivotal role in genome evolution, offering a poetic opportunity for the acquisition of new functional genes. However, only a select duplicated genes manage to persist and contribute to adaptive genome evolution. This is due to molecular mechanisms that act against the emergence of new genes, such as mutation and recombination. Among these mechanisms, non-homologous gene conversion stands out. Non-homologous gene conversion serves to homogenize DNA sequence variation between the original and duplicated genes, thereby impeding the independent evolution of the two copies. In this presentation, I will introduce theoretical perspectives on the evolutionary trajectory of a new gene, with a particular emphasis on the population genetic processes immediately following gene duplication. Then, I will discuss the conditions under which a new gene can evolve.