Author(s): Thomas Duguet, Andreas Ekström, Richard J. Furnstahl, Sebastian König, and Dean Lee The numerical treatment of quantum systems often requires large amounts of computing power and time. As a result, performing calculations repeatedly for different values of the input parameters is often not feasible. One remedy is using eigenvectors describing the system that are analytic functions that vary smoothly for real values of the input parameters. This allows one to replace computationally expensive calculations with emulators that project onto a reduced-basis set. This Colloquium explores a particular class of reduced-basis methods known as eigenvector continuation and its applications, with emphasis on nuclear physics. [Rev. Mod. Phys. 96, 031002] Published Wed Aug 14, 2024