Abstract: In this talk, I will trace the interplay of science and technology in the context of semiconductor heterostructures and the quantum-hall effect (QHE), culminating in the discovery of the fractional QHE, and unfolding of its complex, hierarchical structure. Following that, I will give an overview of the fascinating phenomena that QHE exemplifies. Finally, as time permits, I will briefly discuss some of the research in this field currently being pursued by several Princeton University groups as part of our unending quest to dig deeper into fundamental physics uncovered as a consequence of the surprising and unexpected discoveries made almost four decades ago."