2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189494A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition of the large N continuum limit. The regularization of arbitrary noncommutative field theories by means of matrix quantum mechanics and its connection to noncommutative solitons is also discussed.22 pages; Based on plenary lecture given at the XXIV Workshop on Geometric Methods in Physics, Bialowieza, Poland, June 26 - July 2 2005. To be published in Journal of Geometry and Symmetry in PhysicsHigh Energy Physics - TheoryMathematical Physicstext