The Anomalous X-ray Pulsars (AXPs) represent our best opportunity to study in detail the physics of magnetars: neutron stars with amazingly strong magnetic fields, so strong, that they fundamentally affect their energetics, evolution and appearance. In order to constraints the processes occurring in magnetar interiors and magnetospheres, I have conducted a phenomenological study of their behaviour.I have observed AXPs in the infrared, optical and X-ray bands, and measured both their variability and global spectral energy distributions. By measuring the interstellar extinction, these spectra do not have the large uncertainties of previous works, and by measuring the distances to the objects, the spectra can be fairly compared. During this work: infrared or optical counterparts have been found for all but one AXP; the brightest source (4U 0142+61) was found to vary rapidly and significantly in each waveband over years of monitoring, yet with no apparent correlations between spectral regions; the contradictions in the previous measures of extinction were resolved; and all six Galactic AXPs had their distances determined and were placed on a map of the Galactic Plane. From these studies, I find that, despite differences among AXPs and their variability in time, some patterns emerge. Perhaps most importantly, the X-ray luminosities of AXPs are very similar, as are their X-ray to infrared flux ratios. In this way, information is starting to mount with which to confront theoretical models, and understand the underlying conditions that give rise to the emission seen.