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Precision astroparticle experiments pose challenges to the conventional picture of homogeneous and isotropic transport of cosmic rays (CRs). The recent detection of the gamma-ray from the TeV Geminga halo is particularly at odds with both the averaged ISM diffusion coefficient and the missing X-ray emission counterpart. I shall start with the modern understanding of MHD turbulence and their interaction with CRs. I will demonstrate the expected CR cross field transport behavior in the presence of 3D MHD turbulence. Both diffusion and superdiffusion can occur depending on the scale of consideration. Then I’ll show that Geminga’s mystery can be understood with anisotropic diffusion in sub-Alfvenic turbulence. The results pinpoint the synergy between CR research and study of turbulence from both theoretical and observational points of view. Multi-wavelength study is not only advantageous, but also necessary.

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