This thesis reports the fabrication and characterisation of thin-film transistors employing conjugated polymers as the semiconductor and solid-state ion conductors as the gate insulator. This type of devices has attracted a lot of attention in recent years, thanks to their ability to generate large currents at low voltages, which is particularly suitable for applications where a large signal amplification is desired. Sensors and active-matrix organic light-emitting diode displays are typical examples where the use of such devices is envisioned. Additionally, the advantages inherent to organic and polymeric materials, for instance low-cost and large-area solution processing, flexibility, transparency and tunability, allows one to envision novel technologies, such as flexible screens, conformable sensor arrays or electronic skin, which necessitate soft materials and could not be developed with the crystalline inorganic semiconductors used in conventional electronics.