In many fields, simulation has grown over the past several decades to become the “third pillar,” together with theory and experimental observations, of scientific inquiry. The ability to predictively model complex phenomena has been revolutionary, leading to new insights in many diverse areas ranging from climate to biology to engineering design. Now, in computing, we are facing our own revolution as the machine capabilities have grown in the last decade from the terascale to the petascale, and are now proposed at the exascale. The underlying architectures of future computers may very well look different from today’s machines; similarly, effectively computing on these machines may require new approaches and “out of the box” thinking by mathematicians, computer scientists, and application specialists working together. In this talk, drawing from my experiences in my career working with domain scientists in several application areas, I will discuss the challenges computational scientists face in the coming years as exascale computing looms and offer solutions to meet those challenges.