The concept of wine complexity has gained considerable interest in recent years, both for wine consumers and wine scientists. As a consequence, some research programs concentrate on the factors that could improve the perceived complexity of a wine. Notably, the possible influence of microbiological factors is particularly investigated. However, wine complexity is a multicomponent concept not easily defined. In this review, we first describe the actual knowledge regarding wine complexity, its perception, and wine chemical composition. In particular, we emphasize that, contrary to expectations, the perception of wine complexity is not related to wine chemical complexity. Then, we review the impact of wine microorganisms on wine complexity, with a specific focus on publications including sensory analyses. While microorganisms definitively can impact wine complexity, the underlying mechanisms and molecules are far from being deciphered. Finally, we discuss some prospective research fields that will help improving our understanding of wine complexity, including perceptive interactions, microbial interactions, and other challenging phenomena.