2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/207967The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.27 pages, 4 figures, to appear in RACSAMFunctional Analysis46B20, 47A12text