The interstellar medium (ISM) of galaxies very often contains a gas component that reaches the temperature of several million degrees, whose physical and chemical properties can be investigated through imaging and spectroscopy in the X-rays. We review the current knowledge on the origin and retention of the hot ISM in star-forming and early-type galaxies, from a combined theoretical and observational standpoint. As a complex interplay between gravitational processes, environmental effects, and feedback mechanisms contributes to its physical conditions, the hot ISM represents a key diagnostic of the evolution of galaxies.

Chapter to appear in the Section "Galaxies" (eds. G. Fabbiano & M. Gilfanov) of Springer's "Handbook of X-ray and Gamma-ray Astrophysics" (eds. C. Bambi & A. Santangelo)