The theory of transport of charged particles in cosmic magnetic fields is at the very center of the investigation of non-thermal phenomena in the universe, ranging from our local neighborhood to supernovae, clusters of galaxies or distant active galaxies. It is crucial to understand how particles get energized to non-thermal energies as well as to describe their motion from the sources to an observer or to another location in the universe. Here I summarize some essential, basic aspects of the theory and discuss some topics in the theoretical framework that are currently being developed. I will also discuss some simple applications of the theory of transport to particle acceleration and propagation in the Galaxy.

51 Pages, to appear in "Foundations of Cosmic Ray Astrophysics", Proceedings of the International School of Physics "Enrico Fermi", Course 208, Varenna, 24-29 June 2022, edited by F. Aharonian, E. Amato, and P. Blasi