The miniaturization of traditional silicon-based electronics will soon reach its limitation as quantum tunneling and heat become serious problems at the several-nanometer scale. Crafting integrated circuits via self-assembly of electronically active molecules using a "bottom-up" paradigm provides a potential solution to these technological challenges. In particular, integrated biomolecular circuits (IbC) offer promising advantages to achieve this goal, as nature offers countless examples of functionalities entailed by self-assembly and examples of controlling charge transport at the molecular level within the self-assembled structures. To this end, the review summarizes the progress in understanding how charge transport is regulated in biosystems and the key redox-active amino acids that enable the charge transport. In addition, charge transport mechanisms at different length scales are also reviewed, offering key insights for controlling charge transport in IbC in the future.