In this talk, we first give a briefy summary of the main topics
in Kaehler geometry related to the existence and uniqueness of the
extremal Kaehler metrics(KE metric is a special case of the ex. Ka.
metric).
 Then we discuss the recent joint work with Tian on Kaehler Ricci flow on
KE manifolds with positive bisectional curvature. We prove that the flow
always converge in such settings.