Synthesis and Growth process of single crystals of BaY 2 F 8 :TR (TR= Nd 3+ ; Pr 3+ ; Er 3+ ; Tb 3+ ;Dy 3+) single-doped and co-doped (Nd 3+ :Dy 3+ ; Nd 3+ :Pr 3+) were performed by Zone Melting method (ZM). The grown crystals were characterized by X-ray diffraction (XRD) and Neutron Diffraction (ND) and analyzed by the Rietveld Method. The melting behavior of this pure and trivalent rare earth doped-fluoride was investigated also by scanning electron microscopy (MEV) and X-ray energy dispersive spectroscopy (EDS). The concentration and distribution of the dopants in the grown crystals were measured, and when feasible, the segregation coefficient was estimated. The single crystals were also analyzed by absorption spectroscopy and emission spectroscopy in the case of the codoped crystals. Evidences of the occurrence of energy transfer process in the UV for Nd-Pr were detected. From the study of the growth process single crystals of 40mm x 10mm in size, with good optical and structural quality were obtained for spectroscopy studies and tests of laser emission. Initial experiments were also performed in the growth of single crystalline fibers of this host doped with Tb 3+ , by the micro-pulling down method aiming a preliminary evaluation of the use of this growth process. Only semi-transparent fibers were obtained. Additional studies are necessary to improve the growth of single crystalline fibers of this fluoride.