A Kähler manifold admits a plethora of metrics. Exhibiting canonical Kähler metrics,, e.g. Kähler-Einstein, constant scalar curvature, etc., and studying their properties is a central problem in Kähler geometry. In this talk, inspired by Calabi’s work, we define a large class of Kähler metrics which we call well-behaved. We will discuss such metric and present several explicit examples and open problems. Finally, we prove a property of well-behaved metrics extending some classical results on Kähler-Einstein metrics and present its consequences.