The spectrum of fluctuations of the geomagnetic field extends from periods of < 10 years to periods of 106 years. Although cycles of constant period appear to be absent, definite segments of the spectrum may be associated with particular phenomena in the core. Secular variation with periods of 10 to 103 years is associated with changes in the nondipole field. Changes in the orientation and intensity of the main dipole contribute to the spectrum at about 104 years. At periods of 105 to 106 years, there may be a contribution from a random walk of the rotation axis. The more recent reversals of the polarity of the main dipole occur at characteristic intervals of about 106 years. The asymmetry of the nondipole component of the present geomagnetic field also appears in the results of new paleomagnetic studies of secular variation in the eastern Pacific basin. Two models for interpreting these results are presented, one based on lateral changes in the electrical conductivity of the lower mantle, and the other on the control of thermal convection patterns in the core by lateral temperature differences in the lower mantle.