Synthetic liquid-like condensates that mimic bio-soft matter condensates formed via liquid-liquid phase separation (LLPS) in living cells have recently attracted significant attention in biophysics and nanobiotechnology. The thermodynamic properties of biomolecular condensates, such as the dependence of stability on weak intermolecular interactions and binding multivalency, have been well studied. However, controlling the dynamic properties of biomolecular condensates remains a major challenge in this field. Liquid-like biomolecular condensates are promising building blocks for protocells, synthetic cells, and synthetic organelles; their dynamic properties and control principles should be explored further. Our group has been studying the dynamic control of nucleic-acid-based, liquid-like condensates. Nucleic-acid-based liquid-like condensates are programmable; their stability, viscoelasticity, and formation efficiency can be tuned by designing nucleic-acid sequences and structures. Recently, we have characterized the dynamic properties of condensates under nonequilibrium conditions, such as their division and fusion. In this talk, we focus on the spatiotemporal control of nucleic-acid-based condensates coupled with enzymatic and nucleic-acid strand displacement reactions. We demonstrate that such spatiotemporal dynamics can provide biomolecular condensates with the computational ability to sense biomolecules, such as microRNAs (miRNAs). Additionally, we show that spatiotemporal dynamics can be extended to the mechanical behaviors of condensates. We believe that spatiotemporal control of nucleic-acid-based condensates will promote the application of dynamic synthetic cells and molecular robots.