The scientific ascent of humankind comes in two forms: incremental progress with traditional thinking, and paradigm transition. The latter typically engenders intense debate, often long lasting, before the transition of the paradigm is deemed acceptable. The magnetospheric discipline is no exception, especially in view of the sparse observations available to reach conclusive theory-data closure. Scientific controversies serve an important role in identifying significant unresolved issues for progress to be made. This review highlights key issues on four controversies present in magnetospheric physics: (1) the on-and-off debate on whether the magnetic field combined with the plasma bulk flow or the electric field combined with the current density is the primary quantity in treating magnetospheric problems; (2) the proper interpretation of transient dayside magnetospheric phenomena, i.e., whether they are related to flux transfer events, plasma transfer events, or solar wind pressure pulses; (3) the physical processes responsible for substorm onset; and (4) justifications for substorms or enhanced magnetospheric convection as the cause of magnetic storms. In issue 1 the merits and limitations of the two approaches are expounded. In issue 2 the predicted similarities and differences between the three interpretations are summarized. In issue 3 the strengths and weaknesses of prominent existing substorm models are elaborated on. In issue 4 the two contributors to storms are recognized and combined. Each controversy has an element of a paradigm transition. The resolutions of these controversies appear to also have one common element in that the presumption of only one theory to be correct may not be valid; a synthesis of existing theories may provide a better understanding of all features associated with the phenomenon. ¿ 2001 American Geophysical Union