Aptamers are strands of DNA or RNA molecules, chemically synthetized and able to bind a wide range of targets, from small molecules to live cells, and even tissues, with high affinity and specificity. Due to their efficient targeting ability, they have many different kinds of applications. Particularly attractive is their use in biotechnology and disease therapy, in substitution of antibodies. They represent a promising way for early diagnosis (aptasensors), but also for delivering imaging agents and drugs and for inhibiting specific proteins (therapeutic aptamers). Starting by briefly reviewing the most recent literature concerning advances in biomedical applications of aptamers and aptasensors, the focus is on the issues of a theoretical/computational framework (proteotronics) for modelling the electrical properties of biomolecules. Some recent results of proteotronics concerning the electrical, topological and affinity properties of aptamers are reviewed.