Inspired by the celebrated C^0, C^2 and C^3 a priori estimate of Calabi, Yau and others on Kaehler Einstein metrics, we will present an expository report of a priori estimates on the constant scalar curvature Kaehler metrics. With this estimate, we prove the Donaldson conjecture on geodesic stability and the properness conjecture on Mabuchi energy functional. This is a joint work with Cheng JingRui.