Although the classical multivariate model is aesthetically enticing, it is not unusual to encounter data sets which do not seem to fit the Gaussian model. A variety of flexible augmentations of the classical model have received attention in recent decades.A full survey will not be attempted. Instead we will concentrate on a few of the directions in which model augmentation has been proposed. Specifically we will discuss: conditional specification, hidden truncation, contour specification and a generalized Rosenblatt construction.