AUTHOR=Lazarian Alex , Xu Siyao , Hu Yue TITLE=Cosmic ray propagation in turbulent magnetic fields JOURNAL=Frontiers in Astronomy and Space Sciences VOLUME=Volume 10 - 2023 YEAR=2023 URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2023.1154760 DOI=10.3389/fspas.2023.1154760 ISSN=2296-987X ABSTRACT=Propagation of cosmic rays (CRs) in {\xu turbulent and magnetized} astrophysical media is a long-standing problem that requires both understanding of the properties of turbulent magnetic fields and their interaction with energetic particles. This review focuses on {\xu selected recent theoretical findings} made based on the %the advances in the field that have been achieved due to progress in understanding and {\xu simulating} magnetohydrodynamic (MHD) turbulence. In particular, we address the problem of perpendicular and parallel propagation of CRs and identify the conditions when the perpendicular propagation is superdiffusive and diffusive. {\xu For the parallel diffusion, we discuss the problems of the traditionally used diffusion mechanism arising from pitch angle scattering and the possible solutions provided by the recently identified ``mirror diffusion" in the presence of turbulent magnetic mirrors.}