Interlocked circular DNA nanostructures, e.g., catenanes or rotaxanes, provide functional materials within the area of DNA nanotechnology. Specifically, the triggered reversible reconfiguration of the catenane or rotaxane structures provides a means to yield new DNA switches and to use them as dynamic scaffolds for controlling chemical functions and positioning functional cargoes. The synthesis of two-ring catenanes and their switchable reconfiguration by pH, metal ions, or fuel/anti-fuel stimuli are presented, and the functions of these systems, as pendulum or rotor devices or as switchable catalysts, are described. Also, the synthesis of three-, five-, and seven-ring catenanes is presented, and their switchable reconfiguration using fuel/anti-fuel strands is addressed. Implementation of the dynamically reconfigured catenane structures for the programmed organization of Au nanoparticle (NP) assemblies, which allows the plasmonic control of the fluorescence properties of Au NP/fluorophore loads associated with the scaffold, and for the operation of logic gates is discussed. Interlocked DNA rotaxanes and their different synthetic approaches are presented, and their switchable reconfiguration by means of fuel/anti-fuel strands or photonic stimuli is described. Specifically, the use of the rotaxane as a scaffold to organize Au NP assemblies, and the control of the fluorescence properties with Au NP/fluorophore hybrids loaded on the rotaxane scaffold, are introduced. The future prospectives and challenges in the field of interlocked DNA nanostructures and the possible applications are discussed.