  We give a review of one of the lines in development of the theory of groups
of finite Morley rank. These groups naturally appear in model theory as
model-theoretic analogues of Galois groups, therefore their actions and their
role as permutation groups is of primary interest. We restrict our story to the
study of connected groups of finite Morley rank $G$ acting in a definably
primitive way on a set $X$ and containing a definable abelian normal subgroup
$V$ which acts on $X$ regularly -- the so-called \emph{primitive groups of
affine type}. For reasons explained in the paper, this case plays a central
role in the theory.
