  The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful
insights on many astrophysical problems. We describe a pseudo-spectral MHD code
suitable for the study of incompressible turbulence. We review our recent works
on direct three-dimensional numerical simulations for MHD turbulence in a
periodic box. In those works, we use a pseudo-spectral code to solve the
incompressible MHD equations. We first discuss the structure and properties of
turbulence as functions of scale. The results are consistent with the scaling
law recently proposed by Goldreich & Sridhar. The scaling law is based on the
concept of scale-dependent isotropy: smaller eddies are more elongated than
larger ones along magnetic field lines. This scaling law substantially changes
our views on MHD turbulence. For example, as noted by Lazarian & Vishniac, the
scaling law can provide a fast reconnection rate. We further discuss how the
study of incompressible MHD turbulence can help us to understand physical
processes in interstellar medium (ISM) by considering imbalanced cascade and
viscous damped turbulence.
