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Cosmic ray propagation is determined by the properties of interstellarturbulence. The multiphase nature of interstellar medium (ISM) and diversity ofdriving mechanisms give rise to spatial variation of turbulence properties.Meanwhile, precision astroparticle experiments pose challenges to theconventional picture of homogeneous and isotropic transport of cosmic rays(CRs). We are opening a new horizon for CR propagation research when studies ofparticle transport and interstellar turbulence confront each other. Here wereview our recent developement on understandings of magnetohydrodynamic (MHD)turbulence and its connection to the fundamental processes governing cosmic raypropagation, different regimes of particle transport, that are augmented withobservational discovery and analysis from multi-wavelength observations.

Magnetohydrodynamic turbulence and propagation of cosmic rays: theory confronted with observations