Abstract: Turbulence is a flow phenomenon existing widely in nature. Therelation between global transport properties and the external driving forcesis the focus of interest for various turbulent flows and heat transfer. Thevariational approach formulated by Doering and Constantin, which yieldsexplicit bounds on global transport in turbulent flow and heat transferdirectly from Navier-Stokes equations, is reviewed in this paper. Theemphasis is on the mathematical analyses of explicit bounds on globaltransport in turbulent shear flow, channel flow and Rayleigh-Benardconvection. Finally, the existing problems and the research prospects inthis field are discussed.