We report the first systematic synthesis of monodisperse rare-earth (RE=La to Lu, Y) fluoride and oxyfluoride nanocrystals with diverse shapes (trigonal REF3 triangular, truncated-triangular, hexagonal, and polygonal nanoplates; orthorhombic REF3 quadrilateral and zigzag-shaped nanoplates; cubic REOF nanopolyhedra and nanorods) from single-source precursors (SSP) of [RE(CF(3)COO)(3)] through controlled fluorination in oleic acid (OA)/oleylamine (OM)/1-octadecene (ODE). To selectively obtain REF3 or REOF nanocrystals, the fluorination of the RE-O bond to the RE-F bond at the nucleation stage was controlled by finely tuning the ratio of OA/ODE or OA/OM, and the reaction temperature. For phase-pure REF3 or REOF naocrystals, their shape-selective syntheses could be realized by further modifying the reaction conditions. The two-dimensional growth of the REF3 nanoplates and the one-dimensional growth of the REOF nanorods were likely due to the selective adsorption of the capping ligands on specific crystal planes of the nanocrystals. Those well-shaped nanocrystals with diverse geometric symmetries (such as D(3h), D(6h), C(2h), O(h), and D(nh)) displayed a remarkable capability to form self-assembled superlattices. By manipulating the solvent-substrate combination, the plate-shaped REF3 nanocrystals could form highly ordered nanoarrays by means of either the face-to-face formation or the edge-to-edge formation. By using this SSP strategy, we also obtained high-quality LaF3:Eu and LaF3:Eu/LaF3 triangular nanoplates that showed photoluminescent red emissions of Eu3+ ions sensitive to the surface effect.