Human milk is a rich source of nutrients and energy, shaped by mammalian evolution to provide all the nutritive requirements of the newborn. In addition, several molecules in breast milk act as bioactive agents, playing an important role in infant protection and guiding a proper development. While major breast milk nutrients such as lactose, lipids and proteins are readily digested and consumed by the infant, other molecules, such as human milk oligosaccharides and glycosylated proteins and lipids, can escape intestinal digestion and transit through the gastrointestinal tract. In this environment, these molecules guide the composition of the developing infant intestinal microbiota by preventing the colonization of enteric pathogens and providing carbon and nitrogen sources for other colonic commensals. Only a few bacteria, in particular Bifidobacterium species, can gain access to the energetic content of milk as it is displayed in the colon, probably contributing to their predominance in the intestinal microbiota in the first year of life. Bifidobacteria deploy exquisite molecular mechanisms to utilize human milk oligosaccharides, and recent evidence indicates that their activities also target other human milk glycoconjugates. Here, we review advances in our understanding of how these microbes have been shaped by breast milk components and the strategies associated with their consumption of milk glycoconjugates.