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In this paper, we present novel methods for exploiting passive and active radially folding mechanisms for reactive and dynamic structures. These enable the application of radially folding structures in domains including fluidics, medical stents, and auxetic materials. A compact form of elastic deployment utilizing linkage strain energy is proposed using beam theory analysis. Elastic strain energy is also shown to produce bistable folding behavior, with two low energy states at full contraction and full expansion, and a bistable switching point at some intermediate position. Polymeric smart materials are investigated for driving active folding. These materials can be readily exploited through the features of the folding structure including its ability to resolve 1-D, 2-D, and 3-D actuation strains into a more effective single degree-of-freedom linear, areal, volumetric or rotational output. The elastic and solid-state nature of many polymeric smart materials means they can implement elastic deployment and bistability. A thermally-activated shape memory polymer is shown to fold a 4-segment structure from expanded to contracted states. Experimental testing of an 8-segment dielectric elastomer actuator prototype demonstrates that radially folding structures can resolve large biaxial planar strains generated by dielectric elastomers into a single linear or rotational output stroke.