This book contains a thorough theoretical consideration of the process of proton channelling through carbon nanotubes. A brief summary of the theoretical and experimental results of studying ion channelling through nanotubes is first discussed. Then, the process of ion channelling is described briefly. After that, the crystal rainbow effect is introduced. A description how it was discovered, and present the theory of crystal rainbows, as the proper theory of ion channelling in crystals and nanotubes is provided. It is shown that the evolution of the angular distribution of channelled protons with the nanotube length can be divided in the cycles defined by the rainbow effect.