Interlocked molecular architectures are well known in supramolecular chemistry and are widely used for various applications like sensors, molecular machines and logic gates. The use of DNA for constructing these interlocked structures has increased significantly within the current decade. Because of Watson-Crick base pairing rules, DNA is an excellent material for the self-assembly of well-defined interlocked nanoarchitectures. These DNA nanostructures exhibit sufficient stability, good solubility in aqueous media, biocompatibility, and can be easily combined with other biomolecules in bio-hybrid nano-assemblies. Therefore, the study of novel DNA-based interlocked systems is of interest for nanotechnology, synthetic biology, supramolecular chemistry, biotechnology, and for sensing purposes. Here we summarize recent developments and applications of interlocked supramolecular architectures made of DNA. Examples illustrating that these systems can be precisely controlled by switching on and off the molecular motion of its mechanically trapped components are discussed. Introducing different triggers into such systems creates molecular assemblies capable of performing logic gate operations and/or catalytic activity control. Interlocked DNA-based nanostructures thus represent promising frameworks for building increasingly complex and dynamic nanomachines with highly controllable functionality.