  We describe a general approach to the theory of self consistent transfer
operators. These operators have been introduced as tools for the study of the
statistical properties of a large number of all to all interacting dynamical
systems subjected to a mean field coupling.
  We consider a large class of self consistent transfer operators and prove
general statements about existence of invariant measures, speed of convergence
to equilibrium, statistical stability and linear response.
  While most of the results presented in the paper are valid in a weak coupling
regime, the existence results for the invariant measures we show also hold
outside the weak coupling regime.
  We apply the general statements to examples of different nature: coupled
continuous maps, coupled expanding maps, coupled systems with additive noise,
systems made of \emph{different maps }coupled by a mean field interaction and
other examples of self consistent transfer operators not coming from coupled
maps.
  We also consider the problem of finding the optimal coupling between maps in
order to change the statistical properties of the system in a prescribed way.
