Biologically sensitive field-effect transistors (BioFETs) are one of the most abundant classes of electronic sensors for biomolecular detection. Most of the time these sensors are realized as classical ion-sensitive field-effect transistors (ISFETs) having non-metallized gate dielectrics facing an electrolyte solution. In ISFETs, a semiconductor material is used as the active transducer element covered by a gate dielectric layer which is electronically sensitive to the (bio-)chemical changes that occur on its surface. This review will provide a brief overview of the history of ISFET biosensors with general operation concepts and sensing mechanisms. We also discuss silicon nanowire-based ISFETs (SiNW FETs) as the modern nanoscale version of classical ISFETs, as well as strategies to functionalize them with biologically sensitive layers. We include in our discussion other ISFET types based on nanomaterials such as carbon nanotubes, metal oxides and so on. The latest examples of highly sensitive label-free detection of deoxyribonucleic acid (DNA) molecules using SiNW FETs and single-cell recordings for drug screening and other applications of ISFETs will be highlighted. Finally, we suggest new device platforms and newly developed, miniaturized read-out tools with multichannel potentiometric and impedimetric measurement capabilities for future biomedical applications.