  Classical nova explosions and type I X-ray bursts are the most frequent types
of thermonuclear stellar explosions in the Galaxy. Both phenomena arise from
thermonuclear ignition in the envelopes of accreting compact objects in close
binary star systems. Detailed observations of these events have stimulated
numerous studies in theoretical astrophysics and experimental nuclear physics.
We discuss observational features of these phenomena and theoretical efforts to
better understand the energy production and nucleosynthesis in these
explosions. We also examine and summarize studies directed at identifying
nuclear physics quantities with uncertainties that significantly affect model
predictions.
