We will provide an overview of the synthesis, structures, chemical and physical properties of novel iron oxides bearing FeO(4) square planar coordination, such as SrFeO(2) and Sr(3)Fe(2)O(5). The preparation of these materials relies on topotactic low-temperature reduction using metal hydrides. For instance, a simple 3D perovskite structure SrFeO(3) converts to a 2D structure SrFeO(2)via SrFeO(2.5). SrFeO(2) shows a remarkable stability against temperature and chemical substitution (for both A- and B-sites) and also tolerates distortions of square planes toward tetrahedra to adapt different A sites. Such structural stability and flexibility arise from strong covalent interactions not only through the in-plane Fe-O-Fe superexchange interactions but also through the out-of-plane Fe-Fe direct exchange interactions, and explains why SrFeO(2) exhibits magnetic order far beyond room temperature. The application of pressure on SrFeO(2) and Sr(3)Fe(2)O(5) further enhances the Fe-Fe direct exchange interactions and eventually induces striking transitions at around 34 GPa: spin-state transition from S = 2 to S = 1, insulator-to-metal transition, and antiferro-to-ferromagnetic transition. The high mobility of oxide ions at relatively low temperatures, during the reduction and reoxidation reaction process would offer an important challenge to tailor and design new solid oxide fuel cells/membranes toward lowering working temperatures.