A hot gaseous halo is predicted from spiral galaxy formation and evolution models, with an extent that could exceed the virial radius. The natural temperature for this gas is approximately the virial temperature, ~2×106 K, where the important lines occur in the X-ray band. This gaseous halo is detected in both X-ray absorption and emission lines with XMM-Newton, Chandra, and Suzaku. The large-scale halo properties are deduced from O VII absorption lines in ~30 sight lines plus O VII and O VIII emission lines in ~700 directions. These observations probe the gaseous halo within about 50 kpc, where a spherical component has a density decline of r-3/2 beyond 3 kpc, with a mean temperature of 2×106 K, and an oxygen metallicity of 0.2-0.9 Solar. This halo gas rotates at about 180 ± 40 km/s in the same direction as the disk. The best-fit includes a hot thick disk with a vertical scale height of 1.3 kpc and a radial scale length of 3 kpc. In the inner part of the halo (< 3 kpc), the Fermi Bubbles drive a weak shock into the gas, leading to a temperature increase in the central region. The thick disk component is a minor mass constituent, but the spherical hot halo has a mass of 3-4×1010 Msun when extrapolated to 250 kpc (the approximate virial radius), comparable to the stellar mass. This does not account for the missing baryons in the Milky Way, which likely lies in hot form at 1-2 virial radii.