Astronomical observations yield rich data of phenomenology on macroscopic scales, while they are typically consequences of microphysical processes on much smaller scales. Many of such processes involve magnetic fields, instabilities and turbulence, and are the subject of computational magnetohydrodynamics (MHD). By properly incorporating the microphysics, I will draw three examples which show that MHD simulations can greatly improve our understandings towards reality, and sometimes lead to surprises. First, I show that the recent simulations on the magneto-rotational instability (MRI) imply that the evolution of accretion disks is likely controlled by the global distribution and transport of magnetic flux. Second, I discuss the gas dynamics in protoplanetary disks and show that non-ideal MHD effects completely suppress the MRI in the inner disk (<10AU), leading to a laminar flow with accretion driven by magneto-centrifugal wind. Finally, I describe a preliminary study of particle acceleration in non-relativistic shocks, which is enabled by capturing the cosmic-ray driven instabilities using charged particles.