Two-dimensional titanium and zirconium trichalcogenides nanosheets with highly anisotropic optoelectronic properties. A serial of two-dimensional titanium and zirconium trichalcogenides nanosheets MX 3 (M = Ti, Zr; X = S, Se, Te) were investigated based on first-principles calculations. The evaluated low cleavage energy indicates that stable two-dimensional monolayers can be exfoliated from their bulk crystals in the experiment. Electronic studies reveal the very rich electronic properties in these monolayers, including metallic TiTe 3 and ZrTe 3 , direct band gap semiconductor, TiS 3 , and indirect band gap semiconductors, TiSe 3 , ZrS 3 and ZrSe 3 . The band gaps of all the semiconductors are between 0.57 and 1.90 eV, which implies their potential applications in nano-electronics. In addition, the calculated effective masses demonstrate the highly anisotropic conduction properties for all the semiconductors. Optically, TiS 3 and TiSe 3 monolayers exhibit good light absorption in the visible and near-infrared region, respectively, indicating their potential applications in optical devices. In particular, the highly anisotropic optical absorption of the TiS 3 monolayer suggests it could be used in designing nano-optical waveguide polarizers.