## 1 Introduction
The development of such molecular machines is based on tailoring the DNA sequences in such a way that the structures firstly self-assemble into desired shapes, and are thereby able to perform predefined tasks via translational or rotational movement. In this respect, dynamic DNA origami devices can be considered analogous to protein shapes and functions that are encoded in the sequences of the polypeptide and nucleic-acid molecules [8]. Importantly, DNA origami provides a straightforward route from sequence design to actual shapes, unlike protein synthesis. However, it is noteworthy that de novo protein design allows the synthesis of completely new proteins with tailored functions [44]. A combination of these two techniques would have potential to revolutionize biomedicine and molecular nanotechnology. In many dynamic systems, the ability to simulate molecular motion and fluctuations becomes increasingly important. There are ways to predict DNA origami dynamics based on rigid-beam models (CanDo) [45; 46], atomistic molecular-dynamics simulation [47], and coarse-grained models (oxDNA) [48; 49]. Additionally, mass-weighted chemical elastic network models (MWCENM) and symmetry-constrained elastic network models (SCENM) [50] can be used to estimate the structural fluctuations. Although the focus of this review is on the DNA origami-based devices, it is noteworthy to mention that diverse DNA-based molecular machines were already introduced years before DNA origami. Famous examples include a machine that performs movement based on a DNA conformation change (DNA switches between B- and Z-forms) [51], and DNA tweezers that can be fueled by additional DNA strands to switch the configuration between open and closed states [52]. By taking advantage of simple DNA nanostructures, it is possible to form nanomechanical devices with different rotational or translational states [53, 54], and to control their movement using, e.g., RNA strands instead of DNA [55]. Later on, DNA nanostructure-based tweezers [56, 57], whose arms can be further equipped with enzymes to facilitate control over chemical reactions were proposed. There are also numerous DNA-based walkers that utilize strand-displacement reactions and employ so-called toehold exchanges. Toeholds are short ssDNA overhangs at the end of dsDNA molecules that firstly bind to reactant ssDNA, i.e., they serve as \"docking sites\" that initiate the strand-displacement reactions. Such devices were extensively reviewed in References [58, 59]. Here, we review dynamic DNA origami devices by dividing the discussion into sections using the criteria of interaction type. In Section 2, we firstly discuss DNA origami assemblies with DNA-DNA interactions, i.e., the mechanical design of DNA origami and the systems that take advantage of strand-displacement reactions, base-stacking interactions, or transient DNA binding. Section 3 is devoted to dynamic DNA origami devices that move due to some other molecular interaction. In other words, the molecular interaction produces a desired movement, or alternatively, the interaction can be characterized using the device as a measurement tool. Section 4 reviews the DNA origami movement due to external stimuli such as light, temperature, pH, and electromagnetic fields, and the devices that can be utilized to probe multiple interactions. Section 5 concludes the discussion and gives future perspectives in this immensely growing field.