Human milk oligosaccharides (HMO) are complex glycans that are present at very high concentrations in human milk but not in infant formula. The significant energy expended by mothers to make these complex glycans suggests they must be important. How do maternal HMOs benefit the breast-fed infant? How are HMOs synthesized in the human mammary gland? How can we provide formula-fed infants with HMOs or HMO-like glycans? This article reviews current knowledge and open questions on the biosynthesis and functions of HMOs.