Identification of two-dimensional (2D) materials in the monolayer limit has led to discoveries of new phenomena and unusual properties. In this lecture, I’ll first report the growth of large-area high-quality 2D ultrathin Mo2C crystals by CVD, which show 2D characteristics of superconducting transitions that are consistent with BKT behaviour and show strong dependence of the superconductivity on the crystal thickness. Furthermore, when we introduce elemental silicon during CVD growth of nonlayered molybdenum nitride, we have obtained centimeter-scale monolayer films of MoSi2N4 which does not exist in nature and exhibits semiconducting behavior, high strength, and excellent ambient stability. On the other hand, we have found that a class of membranes assembled with 2D transition-metal phosphorus trichalcogenide nanosheets give exceptionally high ion conductivity and superhigh lithium ion conductivity. Interestingly, we even demonstrate an anomalously large magneto-birefringence effect in transparent suspension of magnetic 2D crystals, with orders of magnitude larger than that in previously known transparent materials. Moreover, based on this phenomenon, we develop a stable and birefringence-tunable deep-ultraviolet modulator from 2D hexagonal boron nitride which gives rise to a ultra-high specific magneto-optical Cotton–Mouton coefficient, about five orders of magnitude higher than other potential deep-ultraviolet-transparent media. These findings indicate a great promise of 2D materials.