Oligomeric proteins are central to cellular life and the duplication and divergence of their genes is a key driver of evolutionary innovations. The duplication of a gene coding for an oligomeric protein has numerous possible outcomes, which motivates questions on the relationship between structural and functional divergence. How do protein oligomeric states diversify after gene duplication? In the simple case of duplication of a homo-oligomeric protein gene, what properties can influence the fate of descendant paralogs toward forming independent homomers or maintaining their interaction as a complex? Furthermore, how are functional innovations associated with the diversification of oligomeric states? Here, we review recent literature and present specific examples in an attempt to illustrate and answer these questions.