ROSAT observations indicate that approximately half of all nearby groups of galaxies contain spatially extended X-ray emission. The radial extent of the X-ray emission is typically 50-500 h −1 100 kpc or approximately 10-50% of the virial radius of the group. Diffuse X-ray emission is generally restricted to groups that contain at least one early-type galaxy. X-ray spectroscopy suggests the emission mechanism is most likely a combination of thermal bremsstrahlung and line emission. This interpretation requires that the entire volume of groups be filled with a hot, low-density gas known as the intragroup medium. ROSAT and ASCA observations indicate that the temperature of the diffuse gas in groups ranges from approximately 0.3 keV to 2 keV. Higher temperature groups tend to follow the correlations found for rich clusters between X-ray luminosity, temperature, and velocity dispersion. However, groups with temperatures below approximately 1 keV appear to fall off the cluster LX-T relationship (and possibly the LX-σ and σ-T cluster relationships, although evidence for these latter departures is at the present time not very strong.) Deviations from the cluster LX-T relationship are consistent with preheating of the intragroup medium by an early generation of stars and supernovae. There is now considerable evidence that most X-ray groups are real, physical systems and not chance superpositions or large-scale filaments viewed edge-on. Assuming the intragroup gas is in hydrostatic equilibrium, X-ray observations can be used to estimate the masses of individual systems. ROSAT observations indicate that the typical mass of an X-ray group is ∼ 10 13 h100−1