Biological barriers are multicellular structures that precisely regulate the transport of ions, biomolecules, drugs, cells, and other organisms. Transendothelial/epithelial electrical resistance (TEER) is a label-free method for predicting the properties of biological barriers. Understanding the mechanisms that control TEER significantly enhances our knowledge of the physiopathology of different diseases and aids in the development of new drugs. Measuring TEER values within microphysiological systems called organ-on-a-chip devices that simulate the microenvironment, architecture, and physiology of biological barriers in the body provides valuable insight into the behavior of barriers in response to different drugs and pathogens. These integrated systems should increase the accuracy, reproducibility, sensitivity, resolution, high throughput, speed, cost-effectiveness, and reliable predictability of TEER measurements. Implementing advanced micro and nanoscale manufacturing techniques, surface modification methods, biomaterials, biosensors, electronics, and stem cell biology is necessary for integrating TEER measuring systems with organ-on-chip technology. This review focuses on the applications, advantages, and future perspectives of integrating organ-on-a-chip technology with TEER measurement methods for studying biological barriers. After briefly reviewing the role of TEER in the physiology and pathology of barriers, standard techniques for measuring TEER, including Ohm's law and impedance spectroscopy, and commercially available devices are described. Furthermore, advances in TEER measurement are discussed in multiple barrier-on-a-chip system models representing different organs. Finally, we outline future trends in implementing advanced technologies to design and fabricate nanostructured electrodes, complicated microfluidic chips, and membranes for more advanced and accurate TEER measurements.