Understanding how charges move through and between biomolecules is a fundamental question that constitutes the basis for many biological processes. On the other hand, it has potential applications in the design of sensors based on biomolecules and single molecule devices. In this review we introduce the study of the electron transfer (ET) process in biomolecules, providing an overview of the fundamental theory behind it and the different experimental approaches. The ET in proteins is introduced by reviewing a complete electronic characterization of a redox protein (azurin) using electrochemical scanning tunnelling microscopy (ECSTM). The ET process in DNA is overviewed and results from different experimental approaches are discussed. Finally, future directions in the study of the ET process in biomolecules are introduced as well as examples of possible technological applications.