Wearable and skin electronics benefit from mechanically soft and stretchable materials to conform to curved and dynamic surfaces, thereby enabling seamless integration with the human body. However, such materials are challenging to process using traditional microelectronics techniques. Here, stretchable transistor arrays are patterned exclusively from solution by inkjet printing of polymers and carbon nanotubes. The additive, non-contact and maskless nature of inkjet printing provides a simple, inexpensive and scalable route for stacking and patterning these chemically-sensitive materials over large areas. The transistors, which are stable at ambient conditions, display mobilities as high as 30 cm² V⁻¹ s⁻¹ and currents per channel width of 0.2 mA cm⁻¹ at operation voltages as low as 1 V, owing to the ionic character of their printed gate dielectric. Furthermore, these transistors with double-layer capacitive dielectric can mimic the synaptic behavior of neurons, making them interesting for conformal brain-machine interfaces and other wearable bioelectronics.