The ytterbium-doped crystals emitting around 1 μm under laser-diode pumping between 900-980 nm have received an increasing interest in recent years as solid-state laser materials for high power or ultra-fast lasers. In this paper, our main objective is to contribute to Yb3+ -doped fluorides mainly on CaF2 cubic host which are characterized by a high value of the thermal conductivity (9.5 W m-1 K-1) as high as YAG. Yb3+-doped CaF2, mono-doped and concentration gradient fibres were grown by both, the laser heated pedestal growth (LHPG) method and by the Czochralski method. Concerning Yb3+ excited state dynamics, the concentration dependence of the 2F5/2 decay time shows a competition between self-trapping and self-quenching processes. Main parameters useful for a theoretical approach of laser potentiality will be given and laser emission under InGaAs laser-diode pumping will be shown.