Galaxy clusters are the most massive gravitationally bound structures in the Universe. In addition to the thousands of galaxies they contain, observations since the 1960s have revealed that these clusters are filled with a hot (∼10⁷ K), diffuse plasma known as the intracluster medium (ICM). Understanding the thermodynamic evolution of this plasma has been a major focus of astrophysical research. One particularly intriguing feature is the presence of long, magnetised filaments of cold gas that appear to condense out of the hot ICM and flow inward toward the central galaxy—a phenomenon that has challenged theorists for the past two decades.

I will start this talk with a broad introduction to galaxy astrophysics. I will then focus on the physical processes that lead to the formation of multiphase gas in galaxy cluster cores, and explain how feedback from supermassive black holes can drive a cycle of cooling, condensation, and heating.