In this review article we will describe recent developments in statisticaltheory of magnetohydrodynamic (MHD) turbulence. Kraichnan and Iroshnikov firstproposed a phenomenology of MHD turbulence where Alfven time-scale dominatesthe dynamics, and the energy spectrum E(k) is proportional to k^{-3/2}. In thelast decade, many numerical simulations show that spectral index is closer to5/3, which is Kolmogorov's index for fluid turbulence. We review recenttheoretical results based on anisotropy and Renormalization Groups whichsupport Kolmogorov's scaling for MHD turbulence. Energy transfer among Fourier modes, energy flux, and shell-to-shell energytransfers are important quantities in MHD turbulence. We report recentnumerical and field-theoretic results in this area. Role of these quantities inmagnetic field amplification (dynamo) are also discussed. There are newinsights into the role of magnetic helicity in turbulence evolution. Recentinteresting results in intermittency, large-eddy simulations, and shell modelsof magnetohydrodynamics are also covered.
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