Knots and links are ubiquitous and constantly provide inspiration in all spheres of human endeavor. For chemists, the synthesis of entangled and interlocked molecules represents a significant challenge, but also an excitingly grand pursuit. We have been working on construction of topological nucleic acid structures using the methodologies and principles developed in the field of structural DNA nanotechnology. According to the rigidity of the systems, different aspects should be considered. Specifically, nucleic acid topological structures have been created at three different levels with different nucleic acid structures. Level 1: Single-stranded (ss) structures. Topological construction with the highly flexible ss nucleic acids basically deals with the problem of how to generate nodes with the desired handedness and in the correct location. To achieve this, we have developed a more general and controllable strategy based on the stacked X-structure of nucleic acid four-way junctions (4WJs) by realizing that the two helical strands within a 4WJ form a node. The handedness of nodes can be readily controlled by manipulating the 4WJs within geometrical constraints, such as forming the tensegrity triangles. Level 2: Double-stranded (ds) structures. At this level, aside from the node formation, embodiment of topology also necessitates the consideration of 3D geometry. Therefore, curvature and torsion of the ds structures should be carefully designed when ss structures are converted to the double-stranded version. Level 3: Self-assemble structures. Self-assembled nucleic acid nanostructures can be rigid enough for enabling the topological construction solely via geometrical control. We have designed a T-shaped RNA branched kissing loop (bKL) structural motif, in which a hairpin loop and a bulge form programmable Watson-Crick base-pairings. Tiles based on this bKL motif permit the control over curvature and torsion of the assemblies. This ultimately allows us to design tiles which can assemble into topologically complex nanostructures. DNA topology is a prominent and fundamental theme in modern biology, and largely defines the structural, biological and functional principles of DNA and most DNA-processing enzymes. Synthetic DNA topological structures can provide invaluable tools to reveal how the problems of DNA topology are tackled in living cells. Meanwhile, the existence of naturally occurring RNA structures with nontrivial topologies remains an enigma. Synthetic RNA topological structures are significant for understanding the physical and biological properties pertaining to RNA topology, and these structures in turn could facilitate identifying naturally occurring knotted or interlocked RNAs. Indeed, RNA topology is an important but unfortunately neglected subject in current research of RNA biology. While constructing self-assembled topological structures (level 3), we have also attempted to study some artificially designed RNA nanostructures with single-crystal X-ray diffraction. The initial goal of these efforts was to obtain high-resolution 3D structural information of the new motif bKL, but eventually we realize that our approach may be developed into a geometry-promoted strategy to overcome the challenging RNA crystallization problem. All in all, our studies on synthetic nucleic acid topological structures have yielded not only aesthetically appealing entities, but also practical tools and strategies for solving fundamental questions in biology.