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We review properties of the $q-$Hermite polynomials and indicate their linkswith the Chebyshev, Rogers--Szeg\"{o}, Al-Salam--Chihara, continuous $q-$%utraspherical polynomials. In particular we recall the connection coefficientsbetween these families of polynomials. We also present some useful andimportant finite and infinite expansions involving polynomials of thesefamilies including symmetric and non-symmetric kernels. In the paper we collectscattered throughout literature useful but not widely known facts concerningthese polynomials. It is based on 43 positions of predominantly recentliterature.

On q-Hermite polynomials and their relationship with some other families of orthogonal polynomials