This talk will present an overview of recent progress towards the solution of one of the grand-challenges of modern science: computing the properties of interacting electrons in molecules and solids. I will argue that the theoretical methodology has reached the point where we can say with confidence that the two dimensional Hubbard model captures key aspects of the high transition temperature superconductivity observed in layered copper-oxide compounds and can delineate which phenomena are not accounted for by this model. I will further summarize the current status of our extension of the methods to fully physically realistic systems, emphasizing the areas of theoretical uncertainty and the prospects for resolution.