Since quasars occur at large redshift, they are present a long time ago, more than halfway back to the beginning of the universe. Hence those black holes that powered quasars must still be around. What are they up to today?

Today's active galaxies used to be quasars. Back when the galaxies were very young they had more gas than they do today and this gas could have fed a supermassive black hole at a great rate. This would account for the high luminosity of the quasars. Today the galaxies are still there, but the rate at which gas is fed into the accretion disk surrounding the black hole is much reduced and so the central engine is less active and one has one or the other of the types of active galaxies.