Abstract: In 2006, Arezzo and Pacard proved the existence of cscK metrics on the blow-up at finitely many points of a cscK manifold admitting no non-trivial holomorphic vector fields. In this talk, I will describe the gluing strategy we used to construct balanced constant Chern scalar curvature metrics on the blow-up of a compact balanced Chern-Ricci flat manifold, generalizing Arezzo-Pacard's result to this case. Finally, I will explain how the same gluing strategy can be adapted to construct Chern-Ricci flat balanced metrics on crepant resolutions of Chern-Ricci flat balanced orbifolds. This is a joint work with Federico Giusti.