The discovery of 680-million year old varves by George Williams in South Australia, recording several millennia of fossil solar cycles, is a most exciting development that is bound to make an impact on solar physics. Already new problems of physical understanding have been posed by the 315-year Elatina cycle and the separate 350-year cycle, or undulation (Williams, 1985(Williams, , 1986;;Williams and Sonett, 1985). The Elatina cycle evidences itself multiplicatively in the form of amplitude modulation with a distinctive nonsinusoidal envelope, while the undulation is additive and quasisinusoidal (Bracewell and Williams, 1986). Both of these periodic phenomena are present in historical records of stmspots, but would not have been discerned from modern solar observations, which do not date back far enough. The explanation of two such sharply defined periods, in addition to the less sharply defined 22-year magnetic cycle, will require an understanding of solar physics that we do not yet have. Examples of the impact that the varve discovery is beginning to make are given, and a previously proposed mechanism for driving the activity cycle is extended in terms of a magnetic wave propagated radially outward from a deep torsional oscillator. * Invited Talk to the 2nd Solar Cycle Workshop.