What is the status of developed turbulence?

Developed turbulence which is concerned with the behavior of turbulent flows at high Reynolds numbers for which there is evidence of scaling, is discussed. The 1941 Kolmogorov theory and the invariance properties of the Navier-Stokes equation are considered. The role of real and complex singularities of solutions of the Navier-Stokes equation is examined in connection with small-scale intermittency. Computer simulations provide strong evidence for the existence of singularities in the complex space-time domain. It is shown that the complex space singularities within less than one mean-free-path of the real domain could invalidate the hydrodynamical approximation. Three explanations for the unpredictable character of the turbulence include: (1) loss of uniqueness through singularities, (2) intrinsic stochasticity, and (3) extrinsic stochasticity. The problem of the minimum number of degrees of freedom needed for high Reynolds number flow is considered. The impact on turbulence of attempts to introduce methods based on the phase transition and quantum field theories is assessed.