  We review the properties of six families of orthogonal polynomials that form
the main bulk of the collection called the Askey--Wilson scheme of polynomials.
We give connection coefficients between them as well as the so-called
linearization formulae and other useful important finite and infinite
expansions and identities. An important part of the paper is the presentation
of probabilistic models where most of these families of polynomials appear.
These results were scattered within the literature in recent 15 years. We put
them together to enable an overall outlook on these families and understand
their crucial r\^{o}le in the attempts to generalize Gaussian distributions and
find their bounded support generalizations. The paper is based on 65 items in
the predominantly recent literature.
