The organic carbamates and carbonates are highly desirable compounds that have found a wide range of applications in drug design, medicinal chemistry, material science, and the polymer industry. The development of new catalytic carbonate and carbamate forming reactions, which employ carbon dioxide as a cheap, green, abundant, and easily available reagent, would thus represent an ideal substitution for existing methods. In this review, the advancements in the catalytic conversion of allylic and propargylic alcohols and amines to corresponding five-membered cyclic carbonates and carbamates are summarized. Both the metal- and the organocatalyzed methods are reviewed, as well as the proposed mechanisms and key intermediates of the illustrated carbonate and carbamate forming reactions.