  The local properties of turbulence driven by the magnetorotational
instability (MRI) in rotating, shearing flows are studied in the framework of a
shearing-box model. Based on numerical simulations, we propose that the
MRI-driven turbulence comprises two components: the large-scale shear-aligned
strong magnetic field and the small-scale fluctuations resembling
magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale
component is close to $k^{-2}$, whereas the spectrum of the small-scale
component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While
the spectrum of the fluctuations is universal, the outer-scale characteristics
of the turbulence are not; they depend on the parameters of the system, such as
the net magnetic flux. However, there is remarkable universality among the
allowed turbulent states -- their intensity $v_0$ and their outer scale
$\lambda_0$ satisfy the balance condition $v_0/\lambda_0\sim \mathrm
d\Omega/\mathrm d\ln r$, where $\mathrm d\Omega/\mathrm d\ln r$ is the local
orbital shearing rate of the flow. Finally, we find no sustained dynamo action
in the $\mathrm{Pm}=1$ zero net-flux case for Reynolds numbers as high as
$45\,000$, casting doubts on the existence of an MRI dynamo in the
$\mathrm{Pm}\leq 1$ regime.
