2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103530We present a review on the recent developments concerning rigorous mathematical results on Schrödinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon.Update of the previous versions; some more references added and typos and some minor errors correctedMathematical Physics81Q10, 81Q70text