  In three-dimensional hydrodynamic turbulence forced at large length scales, a
constant energy flux $ \Pi_u $ flows from large scales to intermediate scales,
and then to small scales. It is well known that for multiscale energy injection
and dissipation, the energy flux $\Pi_u$ varies with scales. In this review we
describe this principle and show how this general framework is useful for
describing a variety of turbulent phenomena. Compared to Kolmogorov's spectrum,
the energy spectrum steepens in turbulence involving quasi-static magnetofluid,
Ekman friction, stable stratification, magnetohydrodynamics, and solution with
dilute polymer. However, in turbulent thermal convection, in unstably
stratified turbulence such as Rayleigh-Taylor turbulence, and in shear
turbulence, the energy spectrum has an opposite behaviour due to an increase of
energy flux with wavenumber. In addition, we briefly describe the role of
variable energy flux in quantum turbulence, in binary-fluid turbulence
including time-dependent Landau-Ginzburg and Cahn-Hillianrd equations, and in
Euler turbulence.
