Glucose sensing has been studied for more than half a century, leading many to believe that further progress comes mainly from engineering efforts. Our society requires robust, reliable, compact, and easy-to-use sensing solutions for decentralized applications such as wearables, and engineering solutions are essential. However, true progress is only possible by understanding and improving the underlying working principles and fundamental limitations. This Perspective discusses the delicate relationship between the observed current and glucose concentration when using wired enzyme biosensors. Some of the potential pitfalls often encountered in the recent literature are discussed. These include the need to suppress the influence of enzyme turnover kinetics on the sensor signal and the undesired faradaic charging of the electron transfer mediator that gives a continuously decaying baseline signal. These fundamental issues must be carefully evaluated and resolved for the realization of continuously operating enzyme biosensor systems.