As thin-film transistors (TFTs) are the workhorse of thin-film electronics, a great deal of focus has been placed upon improving their performance. One major avenue of investigation is the use of electrolyte dielectrics, which can form high capacitance electric-double layers (EDLs). The high capacitance of the EDL enables low-voltage TFT operation by inducing high carrier densities in the channel at low operating voltages. Moreover, due to the diverse range of electrolyte materials under investigation, many EDL TFTs meet the requirements for use in flexible and printable electronics. Here, the basic principles of TFTs and EDLs are introduced along with the advantages and disadvantages of different types of electrolytes. The present status of EDL TFTs is assessed with respect to different channel materials, e.g. oxide semiconductors and organic semiconductors. An overview of the potential uses of EDL is also given, including research into insulator-to-metal and insulator-to-superconductor transitions as well as incorporation into both chemical and thermal sensors. Beyond the basic EDL TFT building blocks, logic circuits for low-power electronic devices, such as memories, sensors, and neuromorphic circuits, which take advantage of the unusual properties of the EDL to mimic neural networks, are also summarized. Finally, the outlook and challenges for EDL TFTs are discussed.