  In this review, we take the reader on a journey. We start by looking at the
properties of galaxies in the cores of rich clusters. We have focused on the
overall picture: star formation in clusters is strongly suppressed relative to
field galaxies at the same redshift. We will argue that the increasing activity
and blue populations of clusters with redshift results from a greater level of
activity in field galaxies rather than a change in the transformation imposed
by the cluster environment. With this in mind, we travel out from the cluster
focussing firstly on the properties of galaxies in the outskirts of clusters
and then on galaxies in isolated groups. At low redshift, we are able to
efficiently probe these environments using the Sloan and 2DF redshift surveys.
These allow an accurate comparison of galaxy star formation rates in different
regions. The current results show a strong suppression of star formation above
a critical threshold in local density. The threshold seems similar regardless
of the overall mass of the system. At low redshift at least, only galaxies in
close, isolated pairs have their star formation rate boosted above the global
average. At higher redshift, work on constructing homogeneous catalogues of
galaxies in groups and in the infall regions of clusters is still at an early
stage. In the final section, we draw these strands together, summarising what
we can deduce about the mechanisms that transform star forming field galaxies
into their quiescent cluster counter-parts. We discuss what we can learn about
the impact of environment on the global star formation history of the universe.
