In this talk I will present different types of inverse and PDE-constrained optimization problems for multiphase tumour growth models which are of some interest for clinical applications. In particular, I will present the inverse identification problem of the initial condition from a single-point measurement at a final time for a Cahn-Hilliard type model describing tumour evolution in the a-vascular stage, and the parameters optimization problem for a multiphase model describing tumour growth in the vascular stage. I will show both analytical and numerical results, and present patient-specific test cases where the optimization problem is based on longitudinal neuroimaging data.