Two-photon absorption (2PA) and two-photon excited fluorescence (2PEF) have received extensive attention due to their potential applications in the fields of high-resolution bioimaging, photodynamic therapy, optical power limiting, three-dimensional microfabrication and high-capacity data storage, etc. Innovative preparation of novel 2PA materials involves nonlinear optical characterization, photophysical studies and the underlying structure-property relationships. 2PA and 2PEF feature the characteristics of interdisciplinary and cross-fields. Aiming to prompt the development of 2PA mechanics and guide for designing efficient 2PA materials, we identify several key questions related to the photophysical processes and characterization methods of 2PA. The effect of laser characteristics on the nonlinear results is illustrated based on our research contributions and the future perspective and challenges in this field are also pointed out.