  Several formulations have long existed in the literature in the form of
continuous mixtures of normal variables where a mixing variable operates on the
mean or on the variance or on both the mean and the variance of a multivariate
normal variable, by changing the nature of these basic constituents from
constants to random quantities. More recently, other mixture-type constructions
have been introduced, where the core random component, on which the mixing
operation operates, is not necessarily normal. The main aim of the present work
is to show that many existing constructions can be encompassed by a formulation
where normal variables are mixed using two univariate random variables. For
this formulation, we derive various general properties. Within the proposed
framework, it is also simpler to formulate new proposals of parametric families
and we provide a few such instances. At the same time, the exposition provides
a review of the theme of normal mixtures.
