Carbon monoxide-releasing molecules (CORMs) that enable the delivery of controlled amounts of CO are of strong current interest for applications in biological systems. In this review, we examine the various conditions under which CO is released from 3-hydroxyflavones and 3-hydroxy-4-oxoquinolines to advance the understanding of how these molecules, or derivatives thereof, may be developed as CORMs. Enzymatic pathways from quercetin dioxygenases and 3-hydroxy-4-oxoquinoline dioxygenases leading to CO release are examined, along with model systems for these enzymes. Base-catalyzed and non-redox-metal promoted CO release, as well as UV and visible light-driven CO release from 3-hydroxyflavones and 3-hydroxy-4-oxoquinolines, are summarized. The visible light-induced CO release reactivity of recently developed extended 3-hydroxyflavones and a 3-hydroxybenzo[g]quinolone, and their uses as intracellular CORMs, are discussed. Overall, this review provides insight into the chemical factors that affect the thermal and photochemical dioxygenase-type CO release reactions of these heterocyclic compounds.