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

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