The planetary magnetic field of Saturn has been studied by the spacecraft Pioneer 11 in 1979, Voyager 1 in 1980, and Voyager 2 in 1981. The field is found to be primarily dipolar and axially concident with the rotation axis but with significant quadrupole and octupole moments. The harmonic terms are g10=21535 nT, g20=1642 nT, and g30=2743 nT. This model field, Z3 in conjunction with a model for an equatorial ring current represents very precisely the in situ magnetic field measurements and data on charged particle absorption by satellites and rings within 8 Rs of the planet. However, this axisymmetric model fails to explain the periodic modulation of Saturn's kilometric radiation (SKR) or Saturn's electrostatic discharges (SED).This enigma of Saturn's magnetosphere remains unsolved in spite of extensive reconsideration of all available data bearing on this issue.