In this talk, the speaker will present recent advances in mathematical modeling and numerical simulation of lung ventilation. The discussion will focus on two components: (1) a fluid dynamics model for airflow through the bronchial tree, incorporating elastic boundary conditions derived from pressure–volume relationships to capture lung elastance and airway resistance, and (2) a 3D hyperelastic-poroelastic model for simulating lung parenchyma deformation. The latter leverages CT imaging data from porcine lungs to construct anatomically realistic geometries and boundary conditions. The speaker will outline the technical framework behind our modeling approach, highlight simulation results, and discuss how to develop digital twins for lung ventilation.