  This work is a review with proofs of a group of results on the stochastic
Burgers equation with small viscosity, obtained during the last two decades.
These results jointly show that the equation makes a surprisingly good model of
hydrodynamical turbulence. The model provides natural and rigorously justified
analogies of a number of key predictions of the theory of turbulence, including
the main assertions of the Kolmogorov approach to turbulence, known as the K41
theory.
