Thirty years ago, scientists first developed computer programs that could tackle the complicated problem of simulating earthquakes as dynamic rupture processes, and predicting the ensuing fault movement. At first, only a few people were able to formulate the appropriate numerical solutions, but these researchers were working with methods that could rarely simulate the full three-dimensional world in which real earthquakes occur. Now, three decades later, our computational infrastructure has vastly improved, along with our knowledge about how to construct computer software that numerically simulates the sudden faulting that occurs during earthquakes. Whereas in the past a lack of computational power provided formidable obstacles, in the present computer capacity is less of a concern, but the science is still hampered by a lack of key field observations, along with critical ideas about the predominant physical processes that control earthquakes.