  In this paper we shall survey the various methods of evaluating Hankel
determinants and as an illustration we evaluate some Hankel determinants of a
q-analogue of Catalan numbers. Here we consider
$\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a q-analogue of Catalan numbers
$C_{n}=\frac1{n+1}\binom{2n}{n}$, which is known as the moments of the little
q-Jacobi polynomials. We also give several proofs of this q-analogue, in which
we use lattice paths, the orthogonal polynomials, or the basic hypergeometric
series. We also consider a q-analogue of Schr\"oder Hankel determinants, and
give a new proof of Moztkin Hankel determinants using an addition formula for
${}_2F_{1}$.
