Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.