Most galaxies host a supermassive black hole (SMBH) at their nucleus. (A supermassive black hole is one whose mass exceeds a million solar-masses.) A key unresolved issue in galaxy formation and evolution is the role these SMBHs play in shaping their galaxies. Most astronomers agree that there must be a strong connection because of the observed correlations between a SMBH’s mass and its galaxy’s luminosity, stellar mass, and the stellar motions in the galaxy. These correlations apply both in local galaxies and those at earlier cosmic epochs. But despite progress in studying SMBHs, how they effect their hosts is still not understood. In some suggested scenarios the SMBH suppresses star formation in the galaxy by expelling material. In others, like the merger scenario, the effect is the opposite: the SMBH boosts star formation by helping stir up the interstellar medium. Computer simulations have been undertaken to try to settle these differences, and they tend to show that cold gas flowing in from the intergalactic medium can feed both SMBH and galaxy growth.