Einstein, EXOSAT, and ROSAT X-ray observations of planetary nebulae detected soft photospheric X-ray emission from their central stars, but the diffuse X-ray emission from the shocked fast stellar wind in their interiors could not be unambiguously resolved. The new generation of X-ray observatories, Chandra and XMM-Newton, have finally resolved the diffuse X-ray emission from shocked fast winds in planetary nebula interiors. Furthermore, these observatories have detected diffuse X-ray emission from bow-shocks of fast collimated outflows impinging on the nebular envelopes, and unexpected hard X-ray point-sources associated with the central stars of planetary nebulae. Here I review the results of these new X-ray observations of planetary nebulae and discuss the promise of future observations.