The intramolecular hydrofunctionalization of carbon-carbon multiple bonds has emerged as a powerful way to form cyclic structures. A particularly important class of reactions involves the use of amine or alcohol nucleophiles, and alkenes or allenes as electrophiles, to form pyrrolidine, piperidine, tetrahydrofuran, and tetrahydropyran heterocycles in a highly efficient manner using late transition metal catalysts. Asymmetric methods for hydroamination and hydroalkoxylation reactions have recently emerged, allowing for the enantioselective synthesis of such saturated heterocycles. This review covers recent developments (over the last 5-10 years) in late transition metal-catalyzed hydroamination and hydroalkoxylation reactions that generate saturated heterocycles.