The GdFeO3-type perovskite NaFeF3 transforms to CaIrO3-type postperovskite at pressures as low as 9 GPa at room temperature. The details of such a transition were investigated by in situ synchrotron powder diffraction in a multianvil press. Fit of the p-V data showed that the perovskite phase is more compressible than related chemistries with a strongly anisotropic response of the lattice metrics to increasing pressure. The reduction in volume is accommodated by a rapid increase of the octahedral tilting angle, which reaches a critical value of 26° at the transition boundary. The postperovskite form, which is fully recoverable at ambient conditions, shows a regular geometry of the edge-sharing octahedra and its structural properties are comparable to those found in CaIrO3-type MgSiO3 at high pressure and temperature. Theoretical studies using density functional theory at the GGA + U level were also performed and describe a scenario where both perovskite and postperovskite phases can be considered Mott-Hubbard insulators with collinear magnetic G- and C-type antiferromagnetic structures, respectively. Magnetic measurements are in line with the theoretical predictions with both forms showing the typical behavior of canted antiferromagnets.