Soft solids capable of conducting ions offer promise for the design of entirely new classes of highly deformable and bio-inspired devices. Here, we introduce ‘ionoelastomers’—soft polymer networks capable of selectively conducting either anions or cations—to demonstrate liquid-free, elastic, and stretchable ionic diodes and transistors that operate entirely via non-Faradaic processes. We show that the junction of two oppositely charged ionoelastomers yields an ‘ionic double layer’, analogous to the depletion layer in a semiconducting p-n junction. Furthermore, soft and stretchable ionoelastomer junctions provide fundamentally new functionalities including: 1) low voltage reversible electro-adhesion and 2) electro-mechanical transduction, i.e., the conversion of mechanical deformation into electrical signals.