Quadratic transformations for orthogonal polynomials in one and two variables

We discuss quadratic transformations for orthogonal polynomials in one and two variables. In the one-variable case we list many (or all) quadratic transformations between families in the Askey scheme or q-Askey scheme. In the two-variable case we focus, after some generalities, on the polynomials associated with root system BC2, i.e., BC2-type Jacobi polynomials if q=1 and Koornwinder polynomials in two variables in the q-case.