Tracking gliomas dynamics on MRI has became more and more important for therapeutic management. Powerful computational tools have been recently developed in this context enabling in silico growth on a virtual brain that can be matched with real 3D segmented evolution through registration between atlases and patient brain MRI data. In this paper, we provide an extensive review of existing algorithms for the three computational tasks involved in patient-specific tumor modeling: image segmentation, image registration, and in silico growth modelling (with special emphasis on the proliferation-diffusion model). Accuracy and limits of the reviewed algorithms are systematically discussed. Finally applications of these methods for both clinical practice and fundamental research are also discussed.