[en] There has been very considerable progress in the last few years on problems that are equivalent to finding the global structure of magnetic field lines in toroidal systems. A general problem of this class has a solution that is so complicated that it is impossible to find equations for the location of a field line which are valid everywhere along an infinitely long line. However, recent results are making it possible to find the asymptotic behavior of such systems in the limit of long lengths. This is just the information that is desired in many situations, since it includes the determination of the existence, or nonexistence, of magnetic surfaces. The key to our present understanding is renormalization. The present state-of-the-art has been described in Robert MacKay's thesis, for which this is an advertisement