This review is intended to account for the experimental and theoretical achievements obtained in a period of about 15 years on the investigation of the electron transport through single redox metalloproteins by scanning probe techniques. A highly focussed research effort has been deployed by the scientists active in this particular field towards measuring and interpreting electronic current signals flowing via blue copper, redox metalloproteins (e.g. azurin). The field has taken a remarkable advantage of the use of electrochemically assisted scanning tunnelling microscope (EC-STM) which has allowed to probe single molecule signals under full control of all the potential values involved in the experiments. This experimental activity has both triggered more comprehensive theoretical interpretations and has been, in its turn, stimulated by theoreticians to test always new predictions. The authors hope to have succeeded in providing the reader with a valuable appraisal of this fascinating field.