In human milk, oligosaccharides are the third largest fraction of components. They are inaccessible for our digestive enzymes and minimally absorbed. Their high concentrations and structural diversity (200+ isoforms) are characteristic for human milk. We explain the composition and terminology and highlight how genetic regulation individually affects human milk oligosaccharide diversity. Human milk oligosaccharides contribute to many benefits of breastfeeding because they may be prebiotic, bind intestinal pathogens reducing infection susceptibility, and modulate the immune system positively. Human milk oligosaccharides are potential substrates for the brain and may promote cognitive development. Technological advances allow producing isolated human milk oligosaccharide isoforms on industrial scale. We review the legal landscape in Europe and whether isolated human milk oligosaccharides could provide benefits.