To simulate real-world processes/systems in a more accurate way, we need to perform multiphysics modeling, involving diverse multiphysics models, such as electromagnetics, mechanics, and heat transfer. This session aims at providing a platform to report recent progress in the advanced numerical algorithms in multiphysics modeling, especially, to deal with its four inherent challenges: nonlinearity (in terms of the constitutive relation), multiple scales (in terms of both time and space), load balancing (in terms of scalable computing), and the associated uncertainty quantification.