I will present the invariance of extremal Kähler manifolds under a suitable class of bimeromorphic morhpisms. This is a joint work with M. Jonsson and S. Boucksom, and it generalizes previous results of Arezzo-Pacard-Singer, Seyyedali-Székelyhidi and Hallam. I will show how our main result is obtained as a consequence of a general uniform coercivity estimate for the Mabuchi energy on the modification, which applies more generally to the class of weighted extremal metrics, modulo a log-concavity assumption on the first weight, and to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose weighted Mabuchi energy is assumed to be coercive.