$100\pmΔt$ Years of Quantum Uncertainty: From Origins to Modern Insights

Abstract: Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations -- known as uncertainty relations -- and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.