The Séminaire de Mathématiques Supérieures (SMS) will be at its 60th anniversary edition in 2021. One of the most well-known summer schools in mathematics in the world, the SMS has the Centre de Recherches Mathématiques (Montreal), the Fields Institute for Research in Mathematical Sciences (Toronto), the Pacific Institute for the Mathematical Sciences (PIMS), and the Mathematical Sciences Research Institute (Berkeley) as its main partners since 2010. It is also supported by the Institut des Sciences Mathématiques (Montreal), the University of Montreal and the Canadian Mathematical Society. The general format of the SMS is a two-week long summer school consisting of approximately twelve mini-courses. The 2021 school on Periodic and Ergodic Spectral Problems will focus on the spectral theory of periodic, almost-periodic, and random operators. The interplay among these topics, which are of fundamental importance in several areas of mathematics and mathematical physics, has become especially active in recent years. The main goal of the school is to teach the participants different methods that are being used in the periodic, almost-periodic and random settings, explain the similarities among them, and show the "big picture".