The conductive polymer poly(3,4-ethylenedioxythiophene) (PEDOT), and especially its complex with poly(styrene sulfonate) (PEDOT:PSS), is perhaps the most well-known example of an organic conductor. It is highly conductive, largely transmissive to light, processible in water, and highly flexible. Much recent work on this ubiquitous material has been devoted to increasing its deformability beyond flexibility-a characteristic possessed by any material that is sufficiently thin-toward stretchability, a characteristic that requires engineering of the structure at the molecular- or nanoscale. Stretchability is the enabling characteristic of a range of applications envisioned for PEDOT in energy and healthcare, such as wearable, implantable, and large-area electronic devices. High degrees of mechanical deformability allow intimate contact with biological tissues and solution-processable printing techniques (e.g., roll-to-roll printing). PEDOT:PSS, however, is only stretchable up to around 10%. Here, the strategies that have been reported to enhance the stretchability of conductive polymers and composites based on PEDOT and PEDOT:PSS are highlighted. These strategies include blending with plasticizers or polymers, deposition on elastomers, formation of fibers and gels, and the use of intrinsically stretchable scaffolds for the polymerization of PEDOT.