Nowadays, the treatment of cancer is based on the so-called diagnostic paradigm. We feel that the shift from the traditional diagnostic paradigm to a predictive patient-specific one may lead to more effective therapies. Thus, the objective of this project is to introduce predictive models for cancer growth. These predictive models will take the form of mathematical models developed from first principles and the fundamental features of cancer biology. For these models to be useful in clinical practice, we will need to introduce new numerical algorithms that permit to obtain fast and accurate simulations based on patient-specific data.We propose to develop mathematical models using the framework provided by the mixtures theory and the phase-field method. Our model will account for the growth of the tumor and the vasculature that develops around it, which is essential for the tumor to grow beyond a harmless limited size. We propose to develop new algorithms based on Isogeometric Analysis, which is a recent generalization of Finite Elements with several advantages. The use of Isogeometric Analysis will simplify the interface between medical images and the computational mesh, permitting to generate smooth basis functions necessary to approximate higher-order partial differential equations like those that govern cancer growth. Our modeling and simulation tools will be examined and validated by experimental and clinical observations. To accomplish this, we propose to use anonymized patient-specific data through several patient imaging modalities.Arguably, the successful undertaking of this project, would have the potential to transform classical population/statistics-based treatments of cancer into patient-specific therapies. This would elevate mathematical modeling and simulation of cancer growth to a stage in which it can be used as a quantitatively accurate predictive tool with implications for clinical practice, clinical trial design, and outcome prediction.