  We review properties of the $q-$Hermite polynomials and indicate their links
with the Chebyshev, Rogers--Szeg\"{o}, Al-Salam--Chihara, continuous $q-$%
utraspherical polynomials. In particular we recall the connection coefficients
between these families of polynomials. We also present some useful and
important finite and infinite expansions involving polynomials of these
families including symmetric and non-symmetric kernels. In the paper we collect
scattered throughout literature useful but not widely known facts concerning
these polynomials. It is based on 43 positions of predominantly recent
literature.
