Spectroscopic, dynamical and thermal properties on Yb3+-doped laser garnets like YAG [1-2], GGG [1-3-4] and LuAG [5] were studied. From experimental decay time dependence, competitive phenomena between two processes have been suggested: the increasing of decay time at low concentration due to the radiative energy transfer (self-trapping) and the decreasing of decay time at higher concentration due to the self-quenching which is connected to the non-radiative energy transfer to impurities (rare earth, OH-, color centers). Yb3+ pairs have also been pointed out and investigated. We have confirmed the quenching mechanisms well described by a limited diffusion process comparable with those of Yb3+-doped sesquioxides. The model has been used to find important parameters for laser application [6]. Laser measurements will be shown under diode pumping. Yb3+-doped GGG or LuAG crystals can be grown with the advantage of high thermal conductivities which will be shown. According to the evaluation recently developed of the new Figure-of-Merit from spectroscopic data [7-8], the potentiality of Yb3+-doped GGG [1] and Yb3+-LuAG [5] as laser crystals in the near infrared is shown better than YAG.