  The asymmetric shape of reversals of the Earth's magnetic field indicates a
possible connection with relaxation oscillations as they were early discussed
by van der Pol. A simple mean-field dynamo model with a spherically symmetric
$\alpha$ coefficient is analysed with view on this similarity, and a comparison
of the time series and the phase space trajectories with those of paleomagnetic
measurements is carried out. For highly supercritical dynamos a very good
agreement with the data is achieved. Deviations of numerical reversal sequences
from Poisson statistics are analysed and compared with paleomagnetic data. The
role of the inner core is discussed in a spectral theoretical context and
arguments and numerical evidence is compiled that the growth of the inner core
might be important for the long term changes of the reversal rate and the
occurrence of superchrons.
