In most accreting black-hole systems the copious X-rays commonly observed from the inner-most regions are accompanied by a reflection spectrum. The latter is the signature of energetic photons reprocessed by the optically thick material of an accretion disk. Given their abundance and fluorescence yield, the iron K-shell lines are the most prominent features in the X-ray reflected spectrum. Their line profiles can be grossly broadened and skewed by Doppler effects and gravitational redshift. Consequently, modeling the reflection spectrum provides one of the best methods to measure, among other physical quantities, the black-hole spin. At present the accuracy of the spin estimates is called into question because the data fits require very high iron abundances: typically several times the solar value. Concurrently no plausible physical explanation has been proffered for these black-hole systems to be so iron rich. The most likely explanation for the supersolar iron abundances is model shortfall at very high densities ($>10^{18}$ cm$^{-3}$) due to atomic data shortcomings in this regime. We review the current observational evidence for the iron supersolar abundance in many black-hole systems, and show the effects of high density in state-of-the-art reflection models. We also briefly discuss our current efforts to produce new atomic data for high-density plasmas, which are required to refine the photoionization models.
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