Classical nova explosions arise from thermonuclear ignition in the envelopes of accreting white dwarfs in close binary star systems. Detailed observations of novae have stimulated numerous studies in theoretical astrophysics and experimental nuclear physics. These phenomena are unusual in nuclear astrophysics because most of the thermonuclear reaction rates thought to be involved are constrained by experimental measurements. This situation allows for rather precise statements to be made about which measurements are still necessary to improve the nuclear physics input to astrophysical models. We briefly discuss desired measurements in these environments with an emphasis on recent experimental progress made to better determine key rates.