Over the years, the modern science of crystallography that started by experimenting with x-ray diffraction from crystals in 1912 has developed a major paradigm: that all crystals are ordered and periodic. Based upon a vast number of experimental data, constantly improving research tools, and deepening theoretical understanding, no revolution was anticipated in our understanding the atomic order of solids. However, such revolution did happen with the discovery, in 1982, of the Icosahedral phase (the first quasi-periodic crystal) by Dr. Shechtman while he was working as a guest researcher at NIST, then NBS. It is clear now that although most crystals are ordered and periodic, a good number of them are ordered and quasi-periodic. Quasi-periodic materials have developed into an exciting interdisciplinary science. In this talk, Nobel Laureate Dan Shechtman will outline the discovery of Quasi-periodic crystals and discuss their structure as well as the role of transmission electron microscopy in the discovery.