Star formation is inherently a 'multiscale' process. In this talk, I will present an overview of my thesis research in molecular cloud and star formation. In particular, I will focus on the MHD, gravitational, and shock dynamical processes related to structure formation in the ISM, from clouds to cores. To model each of these processes, I have used the numerical code, AstroBEAR. AstroBEAR is a powerful multiphysics, adaptive mesh refinement tool developed at the University of Rochester. It is publicly available, free to download, and suitable for a wide-range of astrophysical contexts.