In this talk we will review recent progress in the application of glueing techniques to the construction of Einstein metrics on closed manifolds. We will focus in particular in the case of negatively curved Einstein metrics on Gromov-Thurston manifolds, where the existence of negatively curved Einstein metrics was first proven by Fine-Premoselli in dimension 4 and recently generalized in every dimension n≥4 by Hamenstadt–Jackel. In a first part of this talk we will recall the original motivation for these constructions and will describe the main ideas involved in the proofs. In a second part of this talk we will address some technical issues and discuss recent progress on similar questions.