In this talk, we study the hyponormality of Toeplitz operators on the weighted Bergman spaces, Fock spaces and Newton spaces. Specially, we consider the hyponormal Toeplitz operators Tϕ, where ϕ is a non-harmonic symbol. We present necessary and sufficient conditions for the hyponormality of Tϕ under some assumptions about the coefficients of ϕ. Finally, we characterize the hyponormality of Toeplitz operators by using the properties of symbols.