Introducing twists into carbon nanotube yarns could produce hierarchical architectures and extend their application areas. Here, we utilized such twists to produce elastic strain sensors over large strain (up to 500%) and rotation actuators with high energy density. We show that a helical nanotube yarn can be overtwisted into highly entangled, macroscopically random but locally organized structures, consisting of mostly double-helix segments intertwined together. Pulling the yarn ends completely resolved the entanglement in an elastic and reversible way, yielding large tensile strains with linear change in electrical resistance. Resolving an entangled yarn and releasing its twists could simultaneously rotate a heavy object (30 000 times the yarn weight) for more than 1000 cycles at high speed. The rotational actuation generated from a single entangled yarn produced energy densities up to 8.3 kJ/kg, and maintained similar capacity during repeated use. Our entangled CNT yarns represent a complex self-assembled system with applications as large-range strain sensors and robust rotational actuators.