Eigenvalues of real tensors were introduced by Lim and Qi in 2005, and attracted much attention due to their applications or links with polynomial optimization, quantum mechanics, statistical data analysis, medical imaging, etc. However, the study for complex tensors is at starting stage. In this talk, we propose conjugate partial-symmetric tensors and conjugate super-symmetric tensors, which generalize the classical concept of Hermitian matrices. Necessary and sufficient conditions for their complex forms taken real values are justified, based on which we propose several definitions for eigenvalues of complex tensors. Approximation methods for computing the largest eignevalue and related complex polynomial optimization models are discussed as well.