||G-equation is a popular model in turbulent combustion which describes the propagation of the thin flame front by a advection term and a laminar term. As the planar front corrugates and propagates in time, we study the asymptotic propagation speed called the turbulent flame speed (s_T). For the advection term, we study the growth rate of s_T when the flow intensity is getting larger. For the laminar term, besides the motion in normal direction, we also add the curvature/strain term to see how the growth rate of s_T is bended/quenched. In this talk, I will summarize the previous analytic works on the steady flows, and then I will update some recent numerical works on the unsteady flows.