Graphitic carbon nitride (g-C3N4) is an attractive photocatalyst which has appealing visible light absorption, outstanding layered porous structure, high stability and nontoxicity. Many experimental methods have been developed to modify the pristine g-C3N4 and enhanced photocatalytic activities have been witnessed. First principle calculation based on density functional theory is an effective approach to investigate the structural, electronic, optical and thermodynamic properties of molecules and crystals, which provides important information to elucidate the improved photocatalytic activity of modified g-C3N4 at atomic or unit-cell levels, or even further, to predict the property and photocatalytic activity of experimentally un-synthesized g-C3N4-based photocatalysts. This review is dedicated to this important material, i.e. tri-s-triazine-based g-C3N4 and summarized a panorama of the major advances in the first-principle investigation. The existing challenges and future directions at the forefront of this emerging research hotpot have also been discussed.