In this paper we present bio-inspired smart structures which exploit the actuation of flexible ionic polymer composites and the kirigami design principle. Kirigami design is used to convert planar actuators into active 3D structures capable of large out-of-plane displacement and that replicate biological mechanisms. Here we present the burstbot, a fluid control and propulsion mechanism based on the atrioventricular cuspid valve, and the vortibot, a spiral actuator based on Vorticella campanula, a ciliate protozoa. Models derived from biological counterparts are used as a platform for design optimisation and actuator performance measurement. The symmetric and asymmetric fluid interactions of the burstbot are investigated and the effectiveness in fluid transport applications is demonstrated. The vortibot actuator is geometrically optimised as a camera positioner capable of 360 degree scanning. Experimental results for a one-turn spiral actuator show complex actuation derived from a single degree of freedom control signal.