Detection of X-rays from classical novae, both in outburst and post-outburst, provides unique and crucial information about the explosion mechanism. Soft X-rays reveal the hot white dwarf photosphere, whenever hydrogen (H) nuclear burning is still on and expanding envelope is transparent enough, whereas harder X-rays give information about the ejecta and/or the accretion flow in the reborn cataclysmic variable. The duration of the supersoft X-ray emission phase is related to the turn-off of the classical nova, i.e., of the H-burning on top of the white dwarf core. A review of X-ray observations is presented, with a special emphasis on the implications for the duration of post-outburst steady H-burning and its theoretical explanation. The particular case of recurrent novae (both the standard objects and the recently discovered ones) is also reviewed, in terms of theoretical feasibility of short recurrence periods, as well as regarding implications for scenarios of type Ia supernovae.