In this talk I will review some work we have done on aspects of solid tumour growth. This will consist of three cases studies modelling:
- acid-mediated cell invasion,
- movement through heterogeneous media, with application to glioblastoma,
- colorectal crypt dynamics.
The models range from coupled systems of nonlinear partial differential equations to discrete cell-based models. In each case, results will be compared with experiment and the mathematical challenges raised highlighted.