Since 2021 he is mainly working at UiT The Arctic University of Norway in Tromsø where he is co-director of the newly established Lie-Størmer Center for fundamental structures in computational and pure mathematics.
A central aspect is the analysis of structure preservation by algebraic and combinatorial techniques (B-series and Lie–Butcher series).
Munthe-Kaas received Exxon Mobil Award for best PhD at NTNU, 1989, and the Carl-Erik Frōberg Prize in Numerical Mathematics 1996 for the paper "Lie–Butcher theory for Runge–Kutta Methods".
Munthe-Kaas is the chair of the international Abel prize committee (2018–2022), he is President of the Scientific Council of Centre International de Mathématiques Pures et Appliquées (CIMPA) (2017–present) and he is Editor-in-Chief of Journal Foundations of Computational Mathematics (2017–present).
Munthe-Kaas married Antonella Zanna, an Italian numerical analyst, in 1997; they have four children and a dog.