The purpose of this project was using mathematics to obtain results applicable to different branches of oncology. We developed mathematical models of tumor growth and response to treatment, and we collected imaging and clinical data from cancer patients. We used this data to feed the models and validate them, searching for optimal therapy schemes. We did so for the three pathologies under study, as well as for other problems. Ordinary and partial differential equations were combined with image processing, multiscale modeling, numerical and optimization methods.