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.