The issues a theory of small scale homogeneous turbulence should resolve are summarized and, with emphasis on the differences, the relationship between these goals and results on the asymptotic behavior of randomly driven fluids is discussed. Some new results on the latter problem, obtained by renormalization group techniques and valid to all orders in the “anomalous dimension”, are reported. These results indicate that in spaces of more than two dimensions, unless a certain plausible technical condition is violated, a white noise stochastic force model, in which the correlations of the Fourier components of the force vary as the inverse power of the dimension of the space, gives rise to a Kolmogorov energy spectrum. They also demonstrate that the results obtained by Forster, Nelson, and Stephen are valid to all orders in the anomalous dimension. A special feature of the Kolmogorov spectrum in the renormalization group analysis is noted.