The first examples of silver fluorotellurites, namely, AgTeO₂F and Ag₂(TeO₂F₂), and the first silver fluoride tellurite, Ag₃F₃(TeF₆)(TeO₂)₁₂, have been obtained successfully under mild hydrothermal conditions. AgTeO₂F displays a new 2D structure composed of a 2D silver oxide layer strengthened by 1D [TeO₂F]_∞ chains. Ag₂(TeO₂F₂) exhibits a new 3D construction consisting of a 3D silver oxyfluoride framework with 1D polyhedral ring channels occupied by the isolated TeO₂F₂ groups. Ag₃F₃(TeF₆)(TeO₂)₁₂ features the first 3D neutral [TeO₂]_∞ open framework with 8- and 4-MPR channels along the a-, b- and c-axes. AgTeO₂F and Ag₂(TeO₂F₂) crystallize in the centrosymmetric space group while Ag₃F₃(TeF₆)(TeO₂)₁₂ is in a non-centrosymmetric space group. Ag₃F₃(TeF₆)(TeO₂)₁₂ shows a unique nonlinear optical property with an SHG intensity of about 70% that of commercial KH₂PO₄, while AgTeO₂F and Ag₂(TeO₂F₂) present an apparent linear optical property and their birefringence is calculated as 0.078 and 0.032@1064 nm, respectively. This work further confirms that fluorination in tellurium(IV) oxides can greatly enrich the structural chemistry and optical properties of metal tellurites.