This talk will present state-of-the-art research and development on algorithms for patient-specific surgical training and pre-surgical planning using haptics and augmented reality technologies. These algorithms are used to recreate interactions between virtual surgical tools and complex anatomies of virtual patients to simulate neurosurgical procedures, such as hematoma and brain tumor removal, as well as spinal/cranial bone drilling and spinal fixation. The algorithms to be presented will include (i) image processing of CT and/or MRI scan data of real patients to create virtual patient-specific 3D models, (ii) interactive volume-based 3D graphics and haptics visualization, (iii) parallel computation for simulation of material removal using CUDA, and (iv) parallel multipoint collision detection for realistic haptics rendering.