In this talk,we report on our recent progress of gate-tuned superconductivity and superconductor-insulator transition in FeSe-derived high-Tc superconductors.Firstly,we realized high Tc with a maximum up to 43 K in thin flake of (Li,Fe)OHFeSe single crystals (with initial Tc~25 K) by liquid-ionic gating technique,and observed a striking first-order transition from superconductor to AFM insulator on the strong charge doping region,just at the verge of optimal doping with highest Tc.We also performed electron doping by liquid-ionic-gating technique in FeSe thin flake and achieved an enhancement of Tc up to 48 K (from initially ~10K) with continuously increasing the gate voltage to about 6 V.At some certain carrier concentration,a Lifshitz transition was suggested as the sample suddenly changed from low-Tc to high-Tc phase.Solid electrolytes can also be used in gating method for tuning superconductivity.We enhanced Tc of the FeSe thin flakes to 46 K by using the solid electrolytes as gate dielectric material.In this process,we observed a complete dome-shaped doping-Tc phase diagram of FeSe thin flake and as well as an insulating behavior at high doping level.These results could help researchers to pursuit new path for exploring higher Tc in these materials.