  Since its discovery as an X-ray source with the Einstein Observatory, the hot
X-ray emitting interstellar medium of early-type galaxies has been studied
intensively, with observations of improving quality, and with extensive
modeling by means of numerical simulations. The main features of the hot gas
evolution are outlined here, focussing on the mass and energy input rates, the
relationship between the hot gas flow and the main properties characterizing
its host galaxy, the flow behavior on the nuclear and global galactic scales,
and the sensitivity of the flow to the shape of the stellar mass distribution
and the mean rotation velocity of the stars.
