  This is a brief review of the main results of our recent studies of the
nonlinear evolution of the small-scale MHD dynamo in the high-Prandtl-number
regime and of the structure of the resulting saturated state of the isotropic
homogeneous MHD turbulence. It is emphasized that the MHD regime without a
uniform mean field (as is the case in our studies) is fundamentally different
from the one in which such a field is externally imposed. The ability of the
turbulence to bend and fold the magnetic-field lines leads to the emergence of
a distinctive small-scale structure. The fields are organized in folds of
characteristic length comparable to the size of the largest turbulent eddies
with spatial-direction reversals at the resistive scale. These folds are very
hard to destroy. In the nonlinear regime, the folding structure coexists with
Alfven waves propagating along the folds. The turbulent energy injected by the
forcing is dissipated in part resistively via the small-scale magnetic fields,
and in part viscously via the Alfven waves.
