A central theme in Kähler geometry is the search for canonical Kähler metrics, such as Kähler-Einstein metrics, constant scalar curvature Kähler (cscK for short) metrics, extremal metrics, Kähler-Ricci solutions, etc. The concept of weighted cscK metrics, introduced by Lahdili in 2019, provides a unification of all the above geometric settings. In this talk I will give a panorama of what it is known about these metrics and I will present a criteria for ensuring their existence. This is a joint work with S. Jubert and A. Lahdili.