Mathematics for healthcare and quantitative biomedicine have become increasingly important, and include various aspects such as modelling and simulation. Important biomedical applications include tumor growth, electrophysiology, tissue regeneration, and biomedical engineering. Mechanical interactions between cells and their surrounding extracellular matrix (ECM) play an important role in many biological processes, such as tissue regeneration. It is known that cells probe their environment by applying traction forces and can actively influence the properties of the ECM. At the same time, the properties of the ECM influence cell functions such as cell migration. This interaction between cells and the ECM is fundamental in understanding biomechanical properties. In this talk, I will focus on the mathematical modelling and simulation of cell-hydrogel interactions, where cell migration is modelled by an agent-based model and the hydrogel is described by nonlinear elasticity equations.