Duck breeding in France is directed mainly towards 'foie gras' (duck fatty liver) production. Nowadays the roasted duck, produced from the pure Muscovy, is economically a less important industry. About 95% of foie gras production comes from force-fed mule duck, the remaining 5% being from the Muscovy duck. After an overview of the French economical and technical context of this production, the paper will focus on the genetic aspects of the mule duck, at the level of theoretical knowledge and considering practical applications for selection. As the mule duck is an infertile hybrid between a female common duck (Anas Platyrhynchos) and a Muscovy drake (Cairina moschata), selection approaches are carried out on both parental strains. But to implement selection, genetic parameters (heritability and genetic correlations) and cross-breeding parameters (direct and maternal additive genetic effects, heterosis effect) need to be known. Our review covers both the reproductive mule parental traits, either in pure strain or in cross-breeding, with main results on the dam side for laying, fertility and hatchability and also considers the mule productive traits, such as growth, feather colour, behaviour, feed efficiency, body composition, force-feeding ability and products quality. Genetic variability of mule duck traits can be established from estimates on either the dam's side, on the sire's side, or on both sides simultaneously. This review represents a comparison of fatty duck selection, which is operated by three major private French companies, with outlines of the breeding scheme specificity.