Signalling pathways can be modelled as a biochemical reaction network. When the kinetics are to follow mass-action kinetics, the resulting
mathematical model is a polynomial dynamical system. I will overview approaches to analyse these models with steady-state data using
computational algebraic geometry and statistics. Then I will present how to analyse such models with time-course data using differential
algebra and geometry for model identifiability. Finally, I will present how topological data analysis can be help distinguish models
and data.