In the frontiers of condensed matter physics, pressure is widely adopted as an independent control parameter for tuning states of matters and plays an important role in finding new phenomena and corresponding physics, as well as in testing the relevant theories. Remarkably, a great deal of success has been achieved in searching for new superconductors and uncovering the microphysics for known superconductors. In this brief review, we attempt to describe the progress in high pressure studies of alkaline selenide superconductors AxFe2-ySe2 (A=K, Rb, Tl/Rb).#br#The high-pressure studies of Tl0.6Rb0.4Fe1.67Se2, K0.8Fe1.7Se2 and K0.8Fe1.78Se2 superconductors show that after the ambient-pressure superconducting phase is completely suppressed under about 9 GPa, the reemergence of a pressure-induced superconductivity with a maximum Tc of 48.7 K is observed at ～11 GPa, which is the highest Tc in this kind of superconductor. The systematic investigations on transport and structural properties for K0.8FeySe2 (y=1.7 and 1.78) reveal that a pressure-induced quantum phase transition occurs at pressure between 9.2 GPa and 10.3 GPa, where the antiferromagnetic state with Fermi liquid behavior converts into the paramagnetic state with non-Fermi liquid behavior. Therefore, it is proposed that the observed reemergence of superconductivity at high pressure is probably driven by the quantum critical transition.#br#In addition, some intriguing puzzles on these superconductors and corresponding possible answers are also reviewed from the perspective of high-pressure studies, including the roles of the insulating magnetic phase in developing/stabilizing ambient-pressure and high-pressure superconducting phases and the significance of the pressure-induced antiferromagnetic fluctuation state for the emergency of superconductivity in the high-pressure superconducting phase.