Understanding the complicated non-linear thermal and magnetodynamic processes observed to continuously reshape the solar atmosphere requires the use of three-dimensional computer simulations and numerical experimentation. In this paper, a number of results from the recent generation of 3D numerical models of magnetic flux emergence from the topmost layers of the solar interior to the corona are reviewed. Four main areas are covered: current sheet formation, plasmoid generation and ejection, 3D reconnection and jet launching. Multidimensional computer simulation of MHD and radiative processes in the solar atmosphere is particularly important at present given the high-quality data expected from Solar B and other satellites in the coming years.