Earth's magnetic environment is dominated by its mainly dipolar internally generated magnetic field. The ancient field has permanently magnetized surface rocks and sediments, and these materials yield information about the field direction and strength through time. I explore recently compiled databases of paleomagnetic field intensity to assess uncertainty and bias in the data, create time-varying models of paleomagnetic axial dipole moment, and constrain field generation processes. First, I examine the statistics of absolute paleointensity data for 0-1 Ma. Virtual axial dipole moments (VADMs) from lavas are on average about 10% higher and show greater dispersion than those from archeological materials. Combining data from all igneous sources reveals an apparent bimodality in the VADM's probability density function. An analysis of stochastic models of the geomagnetic field spectrum demonstrate that the bimodality likely arises from long term changes in field strength. Both absolute and relative paleointensity data and a new penalized maximum likelihood approach are used to construct PADM2M, a time-varying model for Paleomagnetic Axial Dipole Moment (PADM) over the past 2 million years. PADM2M has a lower mean than existing VADM reconstructions but has similar long-period variability. The average axial dipole moment over 0-2 Ma is 53 ZAm² with a standard deviation of 15 ZAm². The Brunhes chron average (62 ZAm²) is higher than for earlier epochs of the Matuyama chron (48 ZAm²). PADM2M is used to study rates of change over the past two million years revealing that for periods longer than about 25 ky there is a clear asymmetry in the statistical distributions for growth versus decay rates of the dipole strength. At 36 ky period, average growth rate is about 20% larger than the decay rate, and the field spends 54% of its time decaying, but only 46% growing. These differences are not limited to times when the field is reversing, suggesting that the asymmetry is controlled by fundamental physical processes underlying all paleosecular variation. Finally, I use these techniques to make regional models of axial dipole moment (RADMs) based on geographically clustered data. These have similar long period behavior, but some major differences, especially around geomagnetic excursions