I will briefly review the convergence theory for non-collapsed Einstein 4-manifolds developed by Anderson, Bando-Kasue-Nakajima and Tian around 1990. This was the main precursor for the more recent higher-dimensional theory of Cheeger-Colding-Naber. However, several difficult problems have remained open even in dimension 4. I will focus on the structure of the possible bubbles and bubble trees in the 4-dimensional theory. In particular, I will explain Kronheimer's classical work on gravitational instantons as well as a recent result of Biquard-H concerning the renormalized volume of a 4-dimensional Ricci-flat ALE space.