V.S. Titov, Z. Mikić, C. Downs, R. Lionello, J.A. Linker, J.E. Leake, M.G. Linton

The numerical modeling of the solar corona and of its dynamical phenomena has experienced significant progress in recent years. Present magnetohydrodynamic (MHD) simulations can be run on large spherical grids, include a realistic description of the energy transfer (thermodynamics) in the corona, and are capable of incorporating photospheric measurements as boundary condition for the magnetic field. These capabilities now allow us to model the large-scale magnetic field and plasma distribution of the corona, as well as transient eruptive phenomena such as jets and coronal mass ejections (CMEs) with unprecedented realism. In this talk, I will review some of these simulations and briefly discuss the next steps that lie ahead.