The junctionless transistor consists of a piece of uniformly doped semiconductor with a gate placed between the source and drain contacts and is, therefore, the simplest transistor structure. Because of its simplicity, the junctionless architecture has been used to fabricate devices in a large number of materials, including poly-crystalline semiconductors deposited on various types of substrates. The absence of a need to form source and drain junctions enables the fabrication of stacked vertical transistors or low-temperature top tiers in 3D integrated circuits. Here we describe the physics and applications of junctionless transistors and list the models developed to simulate their electrical properties. The advantages and drawbacks of these devices are described at length, and a long list of references is given to help the Reader find easily the articles published on the different properties of junctionless transistors.