Bioelectronic materials interface biomolecules, cells, organs, or organisms with electronic devices, and they represent an active and growing field of materials research. Protein and peptide nanostructures are ideal bioelectronic materials. They possess many of the properties required for biocompatibility across scales from enzymatic to organismal interfaces, and recent examples of supramolecular protein and peptide nanostructures exhibit impressive electronic properties. The ability of such natural and synthetic protein and peptide materials to conduct electricity over micrometer to centimeter length scales, however, is not readily understood from a conventional view of their amino acid building blocks. Distinct in structure and properties from solid-state inorganic and synthetic organic metals and semiconductors, supramolecular conductive proteins and peptides require careful theoretical treatment and experimental characterization methods to understand their electronic structure. In this review, we discuss theory and experimental evidence from recent literature describing the long-range conduction of electronic charge in protein and peptide materials. Electron transfer across proteins has been studied extensively, but application of models for such short-range charge transport to longer distances relevant to bioelectronic materials are less well-understood. Implementation of electronic band structure and electron transfer formulations in extended biomolecular systems will be covered in the context of recent materials discoveries and efforts at characterization of electronic transport mechanisms.