The Department of Energy’s Council on Materials Science convened a Panel charged with assessing the present scientific understanding of epitaxial growth and identifying fruitful research opportunities in this area. The Panel, chaired by Paul S. Peercy, a member of the Department of Energy’s Council on Materials Science and of the Solid State Sciences Committee, was composed of scientists in materials science, physics, and chemistry from academia, government labs and industry. Panel members were: Ernst G. Bauer, Brian W. Dodson, Daniel J. Ehrlich, Leonard C. Feldman, C. Peter Flynn, Michael W. Geis, James P. Harbison, Richard J. Matyi, Pierre M. Petroff, Paul S. Peercy, Julia M. Phillips, Gerald B. Stringfellow and Andrew Zangwill. The Panel met in January, 1989; its activities were supported by the Materials Sciences Division of Basic Energy Sciences. Deliberations emphasized artificially structured materials and resulted in a Panel Report which has been submitted to the Journal of Materials Research. With permission from the Department of Energy, this article excerpts from the report.