In this talk, I shall first introduce some results on the nonlinear stability for the incompressible rotating fluids in T×R×T near the Couette flow, by precisely quantifying the stability threshold at high Reynolds number. These equations include Navier-Stokes equations and Boussinesq equations. We emphatically show the various beneficial effects by rotation in the linear and nonlinear stability estimates. This talk is based on joint work with Wenting Huang (BNU), Zekai Luo (BNU) and Ying Sun (BUPT).