Remarkable progress in the understanding of nova outbursts has been achieved through combined efforts in photometry, spectroscopy and numerical simulations. According to the thermonuclear runaway model, novae are powered by thermonuclear explosions in the hydrogen-rich envelopes transferred from a low-mass stellar companion onto a close white dwarf star. Extensive numerical simulations in 1-D have shown that the accreted envelopes attain peak temperatures ranging between 108 and 4 × 108 K, for about several hundred seconds, hence allowing extensive nuclear processing which eventually shows up in the form of nucleosynthetic fingerprints in the ejecta. Indeed, it has been claimed that novae can play a certain role in the enrichment of the interstellar medium through a number of intermediate-mass elements. This includes 17O, 15N, and 13C, systematically overproduced with respect to solar abundances, plus a lower contribution in a number of other species (A < 40), such as 7Li, 19F, or 26Al. At the turn of the XXI Century, classical novae have entered the era of multidimensional models, which provide a new insight into the physical mechanisms that drive mixing at the core-envelope interface. In this review, we will present hydrodynamic models of classical novae, from the onset of accretion up to the explosion and ejection stages, both for classical and recurrent novae, with special emphasis on their gross observational properties and their associated nucleosynthesis. The impact of nuclear uncertainties on the final yields will be discussed. Recent results from 2-D models of mixing during classical nova outbursts will also be presented.