Galaxy groups and clusters are the least massive systems where the bulk
of baryons are accounted for and also the most massive systems that are
gravitationally bound. They contain a wealth of galaxies sampling the
broad spectra of galaxy properties, including the most massive galaxies
(and probably the most massive supermassive black holes) and galaxies
with the highest velocities in the universe. Galaxy groups and clusters
are then ideal systems to study cosmic structure formation and the
related baryon physics in multi-phase media. In this talk, I will
summarize our works on two kinds of multi-phase objects with synergy in
galaxy groups and clusters, X-ray cool cores around the central galaxies
and stripped tails behind satellite galaxies. New results from
multi-wavelength data, including those from XRISM, MUSE and a recent
ALMA large program, will be presented, with the implications and future
prospects discussed.