The ion-sensitive field effect transistors (ISFETs), proposed little over 50 years ago, today make the most promising devices for lab-on-a-chip, implantable, and point-of-care (POC) diagnostics. Their compatibility with CMOS (Complementary Metal Oxide Semiconductor) technology and the low cost through mass production have been the driving factors so far. Nowadays, they are also being developed in flexible form factors for new applications such as wearables and to improve the effective usage in existing applications such as implantable systems. In this regard, the CMOS ultra-thin chip (UTC) technology and the bonding by printing are the noteworthy advances. This paper comprehensively reviews such new developments in the CMOS-compatible ISFETs, along with their theory, readout circuitries, circuit-based techniques for compensation of the ISFET's instabilities, such as the offset, flicker noise, and drift. The sensing mechanisms and the properties of interface between the electrolyte under test and the metal-oxide based ion-sensitive electrodes have been discussed along with a brief overview of the metal-oxide based pH sensors. An overview of the reported mechanically flexible pH sensors, including ISFETs, is provided and the history of ISFET applications are also covered. Finally, established models that can be used to design flexible circuits are presented, and possible opportunities to use circuit techniques to compensate for mechanical deformation are discussed.