Numerical Modeling of the Solar Chromosphere and Corona: What Has Been Done? What Should Be Done?

A number of increasingly sophisticated numerical simulations spanning the solar atmosphere from below the photosphere in the convection zone to far above in the corona have shed considerable insight into the role of the magnetic field in the structure and energetics of the Sun's outer layers. This development is strengthened by the wealth of observational data now coming on-line from both ground and space based observatories. In this talk we will concentrate on the successes and failures of the modeling effort thus far and discuss the inclusion of various effects not traditionally considered in the MHD description such as time dependent ionization, non-LTE radiative transfer, and generalized Ohm's law.