We simulate incompressible , MHD turbulence using a pseudo-spectral code .
Our major conclusions are as follows .

1 ) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves .
Shear Alfvén waves control the cascade dynamics .
Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves .
Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves .

2 ) MHD turbulence is anisotropic with energy cascading more rapidly along k _ { \perp } than along k _ { \parallel } , where k _ { \perp } and k _ { \parallel } refer to wavevector components perpendicular and parallel to the local magnetic field .
Anisotropy increases with increasing k _ { \perp } such that excited modes are confined inside a cone bounded by k _ { \parallel } \propto k _ { \perp } ^ { \gamma } where \gamma < 1 .
The opening angle of the cone , \Theta ( k _ { \perp } ) \propto k _ { \perp } ^ { - ( 1 - \gamma ) } , defines the scale dependent anisotropy .

3 ) The 1D inertial range energy spectrum is well fit by a power law , E ( k _ { \perp } ) \propto k _ { \perp } ^ { - \alpha } , with \alpha > 1 .

4 ) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods .
Nevertheless , turbulent fluctuations are small deep inside the inertial range .
Their energy density is less than that of the background field by a factor \Theta ^ { ( \alpha - 1 ) / ( 1 - \gamma ) } \ll 1 .

5 ) MHD cascades are best understood geometrically .
Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves .
Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other .
Shear Alfvén waves are responsible for the mapping ’ s shear and slow waves for its dilatation .
The amplitude of the former exceeds that of the latter by 1 / \Theta ( k _ { \perp } ) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics .

6 ) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations .

7 ) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field .
Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k _ { \perp } by \delta ( t ) correlated forcing .
It appears to be statistically stable to the unlimited growth of imbalance .

8 ) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale .
Sheets formed by oppositely directed waves are uncorrelated .
We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up .

9 ) Items ( 1 ) - ( 6 ) lend support to the model of strong MHD turbulence put forth by Goldreich & Sridhar ( GS ) .
Results from our simulations are also consistent with the GS prediction \gamma = 2 / 3 , as are those obtained previously by Cho & Vishniac .
The sole notable discrepancy is that 1D energy spectra determined from our simulations exhibit \alpha \approx 3 / 2 , whereas the GS model predicts \alpha = 5 / 3 .
Further investigation is needed to resolve this issue .