The Hankel determinants of certain number theoretic sequences have been well-studies; while some q-analogues still remain open. The first results is the Hankel determinants on the q-Euler number, intro- duced by Carlitz in 1948. Similarly to the parallel results of Chapton and Zeng on the q-Bernoulli number, our proof also includes the big q-Jacobi polynomials as the associated orthogonal polynomials. Another result is the Hankel determinant under q-binomial transform. Classical invariant of Hankel determinant under the binomial transform is no longer preserved, when the binomial coefficients are replaced by the q-binomial ones. We obtained the degree and the general formula of the leading coefficient in such Hankel determinants. This is joint work with Shane Chern, Shuhan Li, Liuquan Wang.