Magnetometry, electrical transport, and neutron scattering measurements were performed on single crystals of the Fe4+-containing perovskite-related phase Sr3Fe2O7−δ as a function of oxygen content. Although both the crystal structure and electron configuration of this compound are closely similar to those of well-studied ruthenates and manganates, it exhibits very different physical properties. The fully oxygenated compound (δ=0) exhibits a charge-disproportionation transition at TD=340 K, and an antiferromagnetic transition at TN=115 K. For temperatures T≤TD, the material is a small-gap insulator; the antiferromagnetic order is incommensurate, which implies competing exchange interactions between the Fe4+ moments. The fully deoxygenated compound (δ=1) is highly insulating, and its Fe3+ moments exhibit commensurate antiferromagnetic order below TN∼600 K. Compounds with intermediate δ exhibit different order with lower TN, likely as a consequence of frustrated exchange interactions between Fe3+ and Fe4+ sublattices. A previous proposal that the magnetic transition temperature reaches zero is not supported.