The Advanced Photon Source was commissioned in March 1995 to provide high-brightness ultrastable x-ray photon beams to its user community. The original beam stability specifications were that the source points not move more than 4.5 microns rms vertically and 17 microns rms horizontally. Reductions in coupling, together with planned reductions in emittance and increasing beamline user sophistication, are pushing the envelope of presently achievable beam stabilization methods. While beam stability below the 2-micron rms level is achieved routinely in the band from .016 Hz to 30 Hz in both the vertical and horizontal planes, much remains to be done to reduce this level below 1 micron rms. An additional challenge is to maintain the beam stability for longer time periods, i.e., days to weeks. This paper discusses progress to date on these issues and suggests methodologies for further improvements.