Geobacter spp. can form a biofilm that is more than 20 μm thick on an anode surface by utilizing the anode as a terminal respiratory electron acceptor. Just how microbes transport electrons through a thick biofilm and across the biofilm/anode interface, and what determines the upper limit to biofilm thickness and catalytic activity (i.e., current, the rate at which electrons are transferred to the anode), are fundamental questions attracting substantial attention. A significant body of experimental evidence suggests that electrons are transferred from individual cells through a network of cytochromes associated with cell outer membranes, within extracellular polymeric substances, and along pili. Here, we describe what is known about this extracellular electron transfer process, referred to as electron superexchange, and its proposed role in biofilm anode respiration. Superexchange is able to account for many different types of experimental results, as well as for the upper limit to biofilm thickness and catalytic activity that Geobacter biofilm anodes can achieve.