Abstract. Thermonuclear runaways are at the origin of some of the most energetic and frequent stellar cataclysmic events. In this review talk, we outline our understanding of the mechanisms leading to classical nova explosions and X-ray bursts, together with their associated nucleosynthesis. In particular, we focus on the interplay between nova outbursts and the Galactic chemical abundances (where 13 C, 15 N, and 17 O constitute the likely imprints of many nova outbursts during the overall 10 Gyr of Galactic history), the synthesis of radioactive nuclei of interest for gamma-ray astronomy ( 7 Be-7 Li, 22 Na, or 26 Al), the endpoint of nova nucleosynthesis, based on theoretical and observational grounds, and the recent discovery of presolar meteoritic grains, both in the Murchison and Acfer 094 meteorites, likely condensed in nova shells. Recent progress in the modeling of X-ray bursts as well as an insight into the input nuclear physics requests, for both novae and X-ray bursts, will also be presented.PACS. 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments -26.30.+k Nucleosynthesis in novae, supernovae and other explosive environments -95.85.Pw γ-ray -97.80.Gm Cataclysmic binaries (novae, dwarf novae, recurrent novae, and nova-like objects); symbiotic stars