The non-thermal filaments in the Galactic centre constitute one of the great mysteries of this region of the Galaxy. We summarise the observational data on these filaments and critically review the various theories which currently outnumber the observed filaments. We summarise our theory for the longest of these filaments, the Snake, and discuss the relevance of this model for the other filaments in the Galactic centre region. The physics involved in our model for the Snake involves much of the physics that has dominated the career of Professor Don Melrose. In particular, the diffusion of relativistic electrons in the Snake is determined from the theory of resonant scattering by Alfvén waves.