In the recent decades robotics and computer science have been gaining more and more relevance in all aspects of our lives. In surgery, for example, they gave birth to procedures, impossible to perform otherwise, like the tele-surgery or the nano-surgery. On this regard, these applied sciences already play an important role in assisting the surgeon both in the operative room and, as a support, in the education of young surgeons, but much work has still to be done. In fact in these last years we have seen an extreme change in the traditional training in surgery and the computer-based simulation is one of the main reason of this shift. The spread of Minimally Invasive Surgery (MIS) has brought major improvements in the quality of healthcare, but it has also increased the complexity of the surgical procedures requiring advanced and highly specialized training systems. Moreover these training procedures need to be reiterated during the operational life of surgeons. Therefore, considering the limited availability of cadavers and the public concern with the non-ethical treatment of animals, the traditional approaches to surgical training are drastically limited encouraging the use of surgical simulators based on virtual environments. Healthcare industries and the scientific community in medicine agree indicating the disruptive potential of the application of Virtual Reality (VR) to the training in the medical field. Therefore the next step is the development of surgical simulators with an high level of realism in order to practice complex procedures in a safe environment. Moreover it is decisive that this evolution is done integrating advanced medical imaging and processing, allowing surgeons to practice simulated interventions on patient specific dataset. The increasing importance of MIS techniques will cause a drastic change in pre-operation planning and basic surgical training. In fact, the features of this kind of surgical approach (the workspace limitation, the 2D vision through a laparoscopic camera and the indirect physical interaction with the patient body) make it possible to use a surgical simulator to train, plan or simulate an intervention, reproducing the visual and tactile feedback of the real surgical procedure on a real patient. This paper presents some research and applicative results on Computer Assisted Surgery (CAS) achieved in the framework of EndoCAS, a newly founded Center of Excellence in Pisa. The research has involved: the development of segmentation algorithms for volumetric datasets, the simulation of bone drilling procedures, the modeling of deformable object cuts and deformations and the simulation of rope interactions during a suture procedure in MIS. All these projects were been developed using a new open source library to support the implementation of techniques for simulating deformable objects. Our purpose is to enhance the surgical training with new improved techniques applied both to the medical imaging and to the computer-based simulation in order to carry the surgical training to a next level of realism.