Extensive research on the synthesis and application of triazine derivatives for electroluminescent devices, phosphorescent emitters, hole transport materials for perovskite solar cells, and TADF materials has been published recently. This review covers article data on the modern trends in design of functionalized triazines obtained within the period 2010–2021. Star-shaped aryl(hetaryl) and arylvinyl derivatives of 1,3,5-triazine, their photoluminescence and application for fluorescent sensors to nitro-containing explosives or proton-controlled optical sensors are discussed. Examples of 1,3,5-triazine derivatives exhibiting two-photon absorption, two-photon excited fluorescence and nonlinear optical properties are reviewed. Hyper-branched and linear polymers for multilayer data storage application are reported. The future development of 1,3,5-triazine-based functional materials is undoubtedly related to the creation of more advanced molecules for PhOLEDs, highly effective organic chromophores with thermally activated delayed fluorescence (TADF), and nonlinear optical (NLO) materials as well as ones for energy storage.