Electric discharges occur when a medium that normally does not conduct electricity, such as air, breaks down and becomes partially ionized. A well known example is lightning, but there are also diverse technological applications of electric discharges. They are a special type of plasma (ionized medium) because they are typically far from thermal equilibrium. The numerical modeling of plasmas can be done with particle or fluid methods, but both approaches are computationally challenging. There are widely varying temporal and spatial scales, the evolution is strongly non-linear, and multidimensional and time-dependent modeling is required. I will discuss these challenges and how we currently deal with them, using for example adaptive mesh refinement and fast elliptic PDE solvers, and I will briefly discuss future directions related to model reduction.