The imaging and spectral capabilities of the Chandra X–ray Observatory and XMM–Newton are extremely well suited for studying the remnants of supernovae. High–resolution imaging over the band 0.1–10 keV maps the detailed structure of the supernova remnant, delineates the forward and reverse shock fronts and facilitates proper motion studies of the expanding material. High–resolution spectroscopy enables detailed diagnostics of the emitting plasma, including temperatures, ionization balance and abundances. Spectroscopy also reveals Doppler velocities along the line of sight. Most powerful is the capability for imaging spectroscopy, which can probe the progressive ionization at the shock fronts, the elemental distribution in the ejecta, and Doppler imaging. Examples are drawn from recent studies of oxygen–rich supernova remnants of various ages.