The Allee effect is a theoretical model predicting low growth rates and the possible extinction of small populations. Historically, studies of the Allee effect have focused on demography. As a result, underlying processes other than the direct effect of population density on fitness components are not generally taken into account. There has been heated debate about the potential of genetic processes to drive small populations to extinction, but recent studies have shown that such processes clearly impact small populations over short time scales, and some may generate Allee effects. However, as opposed to the ecological Allee effect, which is underpinned by cooperative interactions between individuals, genetically driven Allee effects require a change in genetic structure to link the decline in population size with a decrease in fitness components. We therefore define the genetic Allee effect as a two‐step process whereby a decrease in population size leads to a change in population genetic structure and, in turn, to a decrease in individual fitness. We describe potential underlying mechanisms and review the evidence for this original type of component Allee effect, using published examples from both plants and animals. The possibility of considering demogenetic feedback in light of genetic Allee effects clarifies the analysis and interpretation of demographic and genetic processes, and the interplay between them, in small populations.