The $M-\sigma$ relation between supermassive black holes and their host
  galaxies
  Supermassive black holes (SMBHs) are found in the centres of most galaxies.
Their masses, and hence their gravitational potentials, are negligible compared
with those of the host galaxy. However, several strong correlations between
SMBH masses and host galaxy properties have been observed, notably the
$M-\sigma$ relation connecting the SMBH mass to the characteristic velocity of
stars in the galaxy. The existence of these correlations implies that the SMBH
influences the evolution of its host galaxy. In this review, we present the
most promising physical model of this influence, known as the Active galactic
nucleus (AGN) wind feedback model. Winds launched from the accretion disc
around the SMBH can drive powerful outflows, provided that the SMBH is massive
enough - this condition establishes the $M-\sigma$ relation. Outflows can have
a profound influence on the evolution of the host galaxy, by compressing its
gas and driving it out, affecting the star formation rate. We present the
current status of the model and the observational evidence for it, as well as
the directions of future research.
