I will discuss canonical metrics on Kahler manifolds, including Kahler-Einstein and constant scalar curvature Kahler metrics. By conjectures of Yau, Tian and Donaldson, the existence of such a metric should be equivalent to the properness of the relevant energy functional and to the algebraic `stability' of the manifold. I will describe some work on energy functionals in Kahler geometry and methods for finding canonical metrics.