This paper is devoted to a survey of wave-particle duality theory of the optical waves and matter waves. The historical notes and the exploration of some paradoxes of this subject are discussed. First,it must be mentioned that the rest mass and the inner construction of photon still be a key problem of science. The papar calls scientits´ attention to that, the wave-particle duality theory established depond on the wavelength being small enough,but the demarcation line is not clear. And so,whether the optical waves and EM waves corresponds to matter, or the character of matter, is discussed. Then, a question for the FTL phase velocity of matter waves is proposed. The analysis shows that how to establish the EM-pulse´s particle image is still to be solved in the future research. Moreover, We connect in the mind, when the EM pulse propagate with a speed higher than the speed of light,will the Special Relativity be disrupted? Finally,the paper presents a discussion on the particlelity of evanescent waves and the virtual photons.