Nucleic acids and proteins are not only biologically important polymers. They have recently been recognized as novel functional materials surpassing conventional materials in many aspects. Although Herculean efforts have been undertaken to unravel fine functioning mechanisms of the biopolymers in question, there is still much more to be done. Here the topic of biomolecular charge transport is presented with a particular focus on charge transfer/transport in DNA and protein molecules. The experimentally revealed details, as well as the presently available theories, of charge transfer/transport along these biopolymers are critically reviewed and analyzed. A summary of the active research in this field is also given, along with a number of practical recommendations.