The Fe-H system has been investigated by combined x-ray diffraction studies and total energy calculations at pressures up to 136 GPa. The experiments involve laser annealing of hydrogen-embedded iron in a diamond anvil cell. Two new FeHx compounds, with x∼2 and x=3, are discovered at 67 and 86 GPa, respectively. Their crystal structures are identified (unit cell and Fe positional parameters from x-ray diffraction, H positional parameters from ab initio calculations) as tetragonal with space group I4/mmm for FeH(∼2) and as simple cubic with space group Pm3m for FeH3. Large metastability regimes are observed that allowed to measure the P(V) equation of state at room temperature of FeH, FeH(∼2), and FeH3.