An intense laser pulse interacting with a near discontinuous plasma vacuum interface causes the plasma surface to perform relativistic oscillations. The reflected laser radiation then contains very high order harmonics of fundamental frequency and-according to current theory-must be bunched in radiation bursts of a few attoseconds duration. Recent experimental results have demonstrated x-ray harmonic radiation extending to 3.3 angstrom (3.8 keV, order n > 3200) with the harmonic conversion efficiency scaling as eta(n) n(-2.5) over the entire observed spectrum ranging from 17 nm to 3.3 angstrom. This scaling holds up to a maximum order, n(RO) 81 8(1/2)gamma(3), where gamma is the peak value of the Lorentz factor, above which the harmonic efficiency decreases more rapidly. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy h nu > 1 keV is found to be into a cone angle similar to 4 degrees, significantly less than that of the incident laser cone (20 degrees).