Interventional MRI scanners now allow neurosurgeons to make images throughout the course of surgery. While these machines are still relatively rare today, they are bound to become a key instrument in the operating theatres of major medical centers. The successful use of such machines requires close collaboration between surgeons and engineers. This presentation describes the problem of neurosurgical navigation and discusses some of its algorithmic challenges, such as the joint use of multiple imaging modalities (CT, MRI, PET, etc), image registration, field-artifact removal, multi-modality image segmentation, biomechanical models of the brain, finite-element models (FEM) for tracking tissue deformation, and a generalization of FEM, known as XFEM, to handle the cuts, retractions, and resections occuring during surgery.