The model anaerobic bacterium, Geobacter sulfurreducens, produces filaments that mediate extracellular electron transfer as part of its respiratory metabolism in oxygen-free environments. The physical, biological, and chemical principles supporting conductivity in protein filaments such as those produced by Geobacter have considerable importance for our understanding of biogeochemical cycles, impacts of climate change, and advanced biomedical devices. We have recently discovered that G. sulfurreducens produces at least three such filaments, which structural studies revealed to be polymers of multiheme cytochromes, OmcS, OmcE, and OmcZ. All three filaments are composed of these cytochrome subunits with bis-histidine-coordinated hemes forming a chain along the fiber axis. Our work aims to understand the structure-property relationships in these conductive filaments, including those that directly support long-range electron transport. Our structural studies show that the arrangement of heme in OmcS and OmcE are nearly identical, despite lacking sequence homology. These two filaments also exhibit heme coordinated across the subunit-subunit interface by histidines from neighboring subunits. The structure of OmcZ is distinct in that it lacks this interfacial heme. One heme per subunit is offset from the axial chain and largely exposed to solvent. Moreover, all heme pairs in these filaments, and indeed most heme pairs within multiheme c-type cytochrome structures in the Protein Databank, cluster into common rotation angle and separation distance arrangement, suggesting conserved electron transfer motifs across domains of life. Spectroscopic comparison between OmcS, OmcE, and OmcZ filaments, and their disassembled monomers will be discussed. Additionally, an outline of the biophysical and electrochemical characterizations of cytochrome filaments and their monomeric subunits will be addressed. The new concepts that will be concluded from the investigation of conductive cytochrome filaments in Geobacter will lead to a better understanding of biological structures supporting long-range electronic conductivity.