Magnetic particle imaging (MPI) is a new emerging medical imaging technique that can be used for cancer diagnosis and treatment. The image produced is a map of superparamagnetic iron oxide nanoparticle tracers that are safe to inject in the human body. This talk will give a tutorial of some of the fundamental concepts in MPI, and particularly those related to the computational signal and image processing pipelines. Theoretical foundations of the methodology will be provided, along with a number of motivating experimental and simulated results on the computational imaging side. Some current and ongoing research will also be discussed.