*MHD Turbulence is common in many space physics and astrophysics environments .
We first discuss the properties of incompressible MHD turbulence .
A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo .
Below equipartition scale for kinetic and magnetic energies the spectrum is steep ( Kolmogorov -5/3 ) and is represented by critically balanced strong MHD turbulence .
In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence .
We measured the efficiency of the small-scale dynamo C _ { E } = 0.05 , Kolmogorov constant C _ { K } = 4.2 and anisotropy constant C _ { A } = 0.63 for MHD turbulence in high-resolution direct numerical simulations .
We also discuss so-called imbalanced or cross-helical MHD turbulence which is relevant for in many objects , most prominently in the solar wind .
We show that properties of incompressible MHD turbulence are similar to the properties of Alfvénic part of MHD cascade in compressible turbulence .
The other parts of the cascade evolve according to their own dynamics .
The slow modes are being cascaded by Alfvénic modes , while fast modes create an independent cascade .
We show that different ways of decomposing compressible MHD turbulence into Alfvén , slow and fast modes provide consistent results and are useful in understanding not only turbulent cascade , but its interaction with fast particles .