Lattice QCD, the fundamental theory of strong interactions and subnuclear structure, was 30 years old last year. Until 2000, however, attempts to analyze the theory numerically were stymied by our inability to simulate efficiently the effects of quark vacuum polarization. Consequently most results had uncontrolled systematic errors of order 15-30% or more. Algorithmic and theoretical developments in the late 1990s led to a breakthrough that makes high-precision, nonperturbative QCD calculations possible for the first time in history. These developments have important implications for heavy-quark and Standard Model physics, and potentially also for our understanding of physics beyond the Standard Model. It also is a major development in the history of quantum field theory. This seminar is a non-technical review of the conceptual ideas behind this revolutionary development in strong-interaction physics, together with a survey of the current impact on theoretical and experimental particle physics, and prospects for the future.