Controlling the contamination of silicon materials by iron, especially dissolved interstitial iron (Fe-i), is a longstanding problem with recent developments and several open issues. Among these, we have the question whether hydrogen can assist iron diffusion or if significant amounts of substitutional iron (Fe-s) can be created. Using density functional calculations, we explore the structure, formation energies, binding energies, migration, and electronic levels of several FeH complexes in Si. We find that a weakly bound FeiH pair has a migration barrier close to that of isolated Fe-i and a donor level at E-v + 0.5 eV. Conversely, FeiH2 (0/+) is estimated at E-v + 0.33 eV. These findings suggest that the hole trap at E-v + 0.32 eV obtained by capacitance measurements should be assigned to FeiH2 . FesH-related complexes show only deep acceptor activity and are expected to have little effect on minority carrier life-time in p-type Si. The opposite conclusion can be drawn for n-type Si. We find that while in H-free material Fe i defects have lower formation energy than Fe-s , in hydrogenated samples Fe-s -related defects become considerably more stable. This would explain the observation of an electron paramagnetic resonance signal attributed to a FesH-related complex in hydrogenated Si, which was quenched from above 1000 degrees C to iced-water temperature.