Field-effect transistors (FETs) have become eminent electronic devices for biosensing applications owing to their high sensitivity, faster response and availability of advanced fabrication techniques for their production. The device physics of this sensor is now well understood due to the emergence of several numerical modelling and simulation papers over the years. The pace of advancement along with the knowhow of theoretical concepts proved to be highly effective in detecting deadly pathogens, especially the SARS-CoV-2 spike protein of the coronavirus with the onset of the (coronavirus disease of 2019) COVID-19 pandemic. However, the advancement in the sensing system is also accompanied by various hurdles that degrade the performance. In this review, we have explored all these challenges and how these are tackled with innovative approaches, techniques and device modifications that have also raised the detection sensitivity and specificity. The functional materials of the device are also structurally modified towards improving the surface area and minimizing power dissipation for developing miniaturized microarrays applicable in ultra large scale integration (ULSI) technology. Several theoretical models and simulations have also been carried out in this domain which have given a deeper insight on the electron transport mechanism in these devices and provided the direction for optimizing performance.