Recently the Event Horizon Telescope (EHT) collaboration reported observing the shadow of a supermassive black hole at the center of a nearby galaxy called M87. But black holes are supposed to be so compact that light cannot escape from them. So how was it possible to observe radio waves coming from the vicinity of the black hole in M87? The answer lies in the dynamics of matter that is accreting into the black hole. Understanding this process requires solving complex equations to describe the flow of matter and the production and propagation of radiation near a black hole. In this talk, I will describe how computational methods running on some of the largest supercomputers in the world have revolutionized our understanding of the accretion of matter into black holes, and allow us to interpret the images from the EHT and other astronomical observations.