Novae have been reported as transients for more than two thousand years. Their bright optical outbursts are the result of explosive nuclear burning of gas accreted from a binary companion onto a white dwarf. Novae containing a white dwarf close to the Chandrasekhar mass limit and accreting at a high rate are potentially the unknown progenitors of the type Ia supernovae used to measure the acceleration of the Universe. Swift X-ray observations have radically transformed our view of novae by providing dense monitoring throughout the outburst, revealing new phenomena in the super-soft X-rays from the still-burning white dwarf such as early extreme variability and half- to one-minute timescale quasi-periodic oscillations. The distinct evolution of this emission from the harder X-ray emission due to ejecta shocks has been clearly delineated. Soft X-ray observations allow the mass of the white dwarf, the mass burned and the mass ejected to be estimated. In combination with observations at other wavelengths, including the high spectral resolution observations of the large X-ray observatories, high resolution optical and radio imaging, radio monitoring, optical spectroscopy, and the detection of GeV gamma-ray emission from recent novae, models of the explosion have been tested and developed. I review nine novae for which Swift has made a significant impact; these have shown the signature of the components in the interacting binary system in addition to the white dwarf: the re-formed accretion disk, the companion star and its stellar wind.