The pressure-induced structural evolution of formamidinium-based perovskite FAPbI(3) was investigated using in situ synchrotron X-ray diffraction and laser excited photoluminescence methods. Cubic alpha-FAPbI(3) (P-m(3) over bar (m)) partially and irreversibly transformed to hexagonal delta-FAPbI(3) (P6(3)mc) at a pressure less than 0.1 GPa. Structural transitions of alpha-FAPbI(3) followed the sequence of Pm (3) over barm -> P4/mbm -> Im (3) over bar -> partial amorphous during compression to 6.59 GPa, whereas the delta-phase converted to an orthorhombic Cmc2(1) structure between 1.26 and 1.73 GPa. During decompression, FAPbI3 recovered the P63mc structure of the 6-phase as a minor component (similar to 18 wt %) from 2.41-1.40 GPa and the Pm (3) over barm structure of the alpha-phase becomes dominant (similar to 82 wt %) at 0.10 GPa but with an increased fraction of delta-FAPbI(3). The photoluminescence behaviors from both the alpha- and delta-forms were likely controlled by radiative recombination at the defect levels rather than band-edge emission during pressure cycling. FAPbI3 polymorphism is exquisitely sensitive to pressure. While modest pressures can engineer FAPbI(3)-based photovoltaic devices, irreversible delta-phase crystallization may be a limiting factor and should be taken into account.