Understanding the ultimate accuracy of EXAFS results includes performing statistical analysis of the estimated parameter errors and minimizing/accounting for the effect of known systematic errors, such as pin holes, self absorption etc. Such known sources of error are considered elsewhere in this volume. Even in the event that all such sources of error are understood and minimized, high-quality EXAFS data are often still not fitted statistically well. In this short chapter, the effect of such unknown errors is considered with ultimate limitations on the accuracy of EXAFS data analysis.