Title: Advances in Numerical Micromagnetics: Adaptive Mesh Refinement, and a problem in Spin Polarized Transfer Abstract: We present a methodology to perform micromagnetics simulations using adaptive mesh refinement. Our approach combines the grid adaptivity, with an unconditionally stable time-stepping scheme. (This project is joint work with Alexandre Roma at the Instituto de Matematica e Estadistica, Sao Paulo, Brasil). I will also discuss some recent progress in the numerical simulation of a model for Spin Polarized Transfer due to Shpiro, Levy, and Zhang. This project is joint work with X.P. Wang at the Hong Kong University of Science and Technology.