The 5d metallocorroles are unusual molecular "misfits" involving a sterically constrained corrole ligand wrapping around a large 5d transition metal ion. In spite of the steric mismatch, many of the complexes are highly stable, both thermally and photochemically. Many, in addition, exhibit long-lived triplet states, NIR phosphorescence, and triplet-triplet annihilation upconversion, and also efficiently sensitize singlet oxygen formation, allowing for applications in photodynamic therapy. Metalloisocorroles with interrupted aromaticity also exhibit efficient photothermal conversion, with potential implications for combined photodynamic and photothermal therapy. Besides describing our major experimental findings in this area, we will also describe DFT calculations aimed at understanding factors governing phosphorescence, or the lack thereof, of metallocorroles and other metalloporphyrin analogues.