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Abstract Computational oceanography is the study of ocean phenomena by numerical simulation, especially dynamical and physical phenomena. Progress in information technology has driven exponential growth in the number of global ocean observations and the fidelity of numerical simulations of the ocean in the past few decades. The growth has been exponentially faster for ocean simulations, however. We argue that this faster growth is shifting the importance of field measurements and numerical simulations for oceanographic research. It is leading to the maturation of computational oceanography as a branch of marine science on par with observational oceanography. One implication is that ultraresolved ocean simulations are only loosely constrained by observations. Another implication is that barriers to analyzing the output of such simulations should be removed. Although some specific limits and challenges exist, many opportunities are identified for the future of computational oceanography. Most important is the prospect of hybrid computational and observational approaches to advance understanding of the ocean.