The spherical aberration of the primary mirror of the Hubble Space Telescope has seriously reduced the sensitivity and degraded the resolution of images and spectra from the instruments onboard the satellite. In this paper, we describe the nature of the aberration problem and the resulting point-spread functions for both the imaging and spectrographic detectors. A number of image restoration algorithms have been evaluated for use on HST data, including both linear and non-linear techniques, and sample results are shown for a modified Richardson- Lucy method. The best prospects for obtaining improvements in the restored images are likely to derive from developing techniques for adaptive regularization.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.