Transition metal carbonyl complexes exhibit a wide-range of vibronic coupling induced phenomena, some of which have only recently begun to be understood via state-of-the-art spectroscopic, as well as theoretical and computational investigations. Historically the Jahn-Teller effect has been used to explain structural information such as ground-state geometries and the lowest energy spin-state. We will review important early work on understanding structural aspects of binary transition metal carbonyl complexes, and then move on to discuss the most recent time-resolved work, and computational studies aimed at explaining these results. The recent time-resolved experiments of have shown that a variety of unexpected features arise from photodissociation of metal carbonyls of the first, second and third rows of the periodic table, and also multiply metal-metal bonded carbonyls. These experiments show that an unsaturated metal carbonyl is produced in the singlet spin-state; the radiationless relaxation being so fast as to preclude a spin-orbit induced change to the high-spin manifold. Such unsaturated metal carbonyls may have accessible geometries that are Jahn-Teller degenerate, and these conical intersections are believed to be the key to ultrafast radiationless decay. This is an exciting development as these systems naturally bring together aspects of the Jahn-Teller effect with photochemistry. Such low-spin degeneracies are not normally found in classical inorganic chemistry; here they are reached photochemically, the exact mechanism from excitation to photoproduct still not fully understood. In relation to modern computational work we discuss current state-of-the-art computational methodologies required to correctly describe metal-carbonyl bonding in the ground and excited states, the resulting potential energy surfaces, and mechanisms of ultrafast photodissociation and subsequent radiationless decay (including conical intersections). We discuss in detail the Jahn-Teller effect in relation to the photochemistry of Cr(CO)6, and Fe(CO)5. Throughout these examples useful group theoretical tools such as the epikernel principle will be exemplified. Several new results will be included at various appropriate points throughout this tutorial review.