Using density-functional theory, we investigate the stability, structural, magnetic, and electronic properties of the iron oxyhydroxide polymorphs [

-,

-,

-, and
hp(

)-FeOOH] under hydrostatic pressure. At ambient conditions goethite (

) is the lowest energy phase, consistent with recent calorimetric measurements. Around 6–7 GPa we predict a transformation to the high-pressure
hp(

) phase. This structural transformation is followed by a high-spin to low-spin transition at 7.7 GPa, at much lower pressure than for other currently discussed iron-bearing minerals. While in the ground state the Fe
3+ ions are coupled antiferromagnetically, at high pressures a strong competition to a ferromagnetic alignment is found in
hp(

)-FeOOH. Concerning the electronic properties, including an on-site Coulomb repulsion parameter
U (LDA/GGA+
U method) improves the size of the zero-pressure band gaps substantially but shifts the spin transition to higher pressure (56.5 GPa). The predicted spin crossover is associated with a blueshift of 0.4 eV.