X-ray absorption studies of QSO sightlines provide evidence for a hot gas (~1e6 K) corona around the Milky Way in the form of highly ionized oxygen (OVII and OVIII). Extended structures of hot gas around galaxies are also suggested by galaxy formation theory and numerical simulations. Recent observations of OVI absorption in the UV show the existence of hot coronae around L* galaxies in the low redshift universe. Due to the challenging nature of the observations, many questions remain open. Where exactly does the gas reside and what are its properties? What is the extent and the total mass of the corona? These questions are important to our understanding of galaxy evolution properties and are linked to a number of other topics such as star formation and stellar feedback, properties of dwarf galaxies (see also Faerman et al. 2013) and IGM gas accretion onto galaxies. We construct a unified model for the hot corona which successfully reproduces a wide range of observations (UV, X-ray and other). In our model, the corona is a large-scale structure, extending to the virial radius of the MW, and has a significant gas mass, ~1e11 M_sun. Such coronae may serve as galactic gas reservoirs, enabling prolonged periods of star formation and, as suggested by previous works, providing a solution to the galactic "missing baryons" problem in the Local Universe.