NASA's 62 teraflops Columbia supercomputer increased the Agency's computing capability ten-fold, revitalized its high-end computing efforts, and enabled scientists and engineers to conduct high-fidelity simulations in diverse areas such as space exploration, Shuttle operations, Earth sciences, and aeronautics research. The talk will describe several applications currently running on Columbia, discuss what could be accomplished with petascale computing, and highlight the architecture and algorithm bottlenecks that must be overcome.