The immense growth in applications of X-ray absorption spectroscopy (XAS) has been enabled by the widespread availability of intense tunable X-rays from synchrotron radiation sources. Recently, new concepts have been proposed for fourth-generation light sources, such as the SASE (self-amplified stimulated emission) X-ray free-electron lasers (XFELs) being pursued at Hamburg (TESLA) and Stanford (LCLS), and the recirculator ring (MARS) at Novosibirsk. These sources offer expected gains of many orders of magnitude in instantaneous brilliance, which will unlock opportunities for qualitatively different science. Examples of new or greatly expanded techniques in XAS could include Raman X-ray absorption fine structure (XAFS), pump-probe experiments, time-resolved XAFS and small-spot X-ray spectromicroscopy, although the limited tunability of the sources might not allow conventional XAFS measurements. Multi-photon X-ray absorption could become a new field of study. There should not be a collective stampede to these new sources, however, and it is likely that storage rings will continue to be necessary for most XAFS applications. The extreme brightness of these future light sources will present difficult challenges in instrumentation, especially detectors and sample containment. Practitioners will also have to exercise caution, because the intensity of the beam will surely destroy many samples and in some cases there will be so many photons absorbed per atom that XAFS will be impossible.