In this talk, we consider Toeplitz operators T_u with symbols of complex Borel measures u, and give a characterization of bounded Toeplitz operators: T_u is bounded if and only if u is a T-Carleson measure when the domain of T_u contains all polynomials. We also obtain similar results for Hankel operators. In addition, we investigate a connection between trigonometric moment problem and Toeplitz operators with symbols of complex Borel measures.