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Recently, 2D tellurene (Te) structures have been experimentally synthesized. These structures possess high carrier mobility and stability which make them ideal candidates for applications in electronics, optoelectronics and energy devices. We performed density functional theory (DFT) and molecular dynamics (MD) simulations to investigate the stability and electronic structure of 2D α- and β-Te sheets, and hydrogen, oxygen, and fluorine functionalized counterparts, including spin–orbit coupling effects. Our calculations show that bare α and β-Te sheets are stable with band gaps of 0.44 eV and 1.02 eV respectively. When functionalized, α and β monolayers exhibit metallic properties, except for hydrogenated β-Te, which exhibits semiconducting properties with a band gap of 1.37 eV. We see that H, O and F destabilize the structure of α-Te. We also find that F and H cause β-Te layers to separate into functionalized atomic chains and O causes β-Te to transform into a Te 3 O 2 -like structure. We also studied single atom and molecule binding on the Te surface, the effects of adatom coverage, and the effects of functionalized Te on a GaSe substrate. Our results indicate that tellurene monolayers and functionalized counterparts are not only suitable for future optoelectronic devices, but can be used as metallic contacts in nanoscale junctions.