Asbtract:  In various applications data can be modelled as a normal mixture, in that the expected value and/or variance may vary among the otherwise independent normal observations. Under certain constraints on the mixing distribution, such normal mixture distributions can be estimated by nonparametic maximum likeihood. Although the mixing distribution is estimated rather poorly, the fitted density is estimated particularly accurately, at an almost parametric rate. This suggests that fitting a normal mixture distribution may work well as a general density estimation method, whether modelling considerations suggest it or not. We review various theoretical results addressing this question from over the last decade, and present some new results pertaining to the multivariate generalisation.