In this paper, we present our view of massively-parallel heterogeneous computing for solving large scientific problems. We start by observing that computing has been the primary driver of major innovations since the beginning of the 21st century. We argue that this is the fruit of decades of progress in computing methods, technology, and systems. A high-level analysis on out-scaling and up-scaling on large supercomputers is given through a time-domain wave-scattering simulation example. The importance of heterogeneous node architectures for good up-scaling is highlighted. A case for low-complexity algorithms is made for continued scale-out towards exascale systems.