The base sequence of nucleic acids encodes structural and functional information into the DNA biopolymer. External stimuli such as metal ions, pH, light, or added nucleic acid fuel strands provide triggers to reversibly switch nucleic acid structures such as metal-ion-bridged duplexes, i-motifs, triplex nucleic acids, G-quadruplexes, or programmed double-stranded hybrids of oligonucleotides (DNA). The signal-triggered oligonucleotide structures have been broadly applied to develop switchable DNA nanostructures and DNA machines, and these stimuli-responsive assemblies provide functional scaffolds for the rapidly developing area of DNA nanotechnology. Stimuli-responsive hydrogels undergoing signal-triggered hydrogel-to-solution transitions or signal-controlled stiffness changes attract substantial interest as functional matrices for controlled drug delivery, materials exhibiting switchable mechanical properties, acting as valves or actuators, and "smart" materials for sensing and information processing. The integration of stimuli-responsive oligonucleotides with hydrogel-forming polymers provides versatile means to exploit the functional information encoded in the nucleic acid sequences to yield stimuli-responsive hydrogels exhibiting switchable physical, structural, and chemical properties. Stimuli-responsive DNA-based nucleic acid structures are integrated in acrylamide polymer chains and reversible, switchable hydrogel-to-solution transitions of the systems are demonstrated by applying external triggers, such as metal ions, pH-responsive strands, G-quadruplex, and appropriate counter triggers that bridge and dissociate the polymer chains. By combining stimuli-responsive nucleic acid bridges with thermosensitive poly(N-isopropylacrylamide) (pNIPAM) chains, systems undergoing reversible solution ↔ hydrogel ↔ solid transitions are demonstrated. Specifically, by bridging acrylamide polymer chains by two nucleic acid functionalities, where one type of bridging unit provides a stimuli-responsive element and the second unit acts as internal "bridging memory", shape-memory hydrogels undergoing reversible and switchable transitions between shaped hydrogels and shapeless quasi-liquid states are demonstrated. By using stimuli-responsive hydrogel cross-linking units that can assemble the bridging units by two different input signals, the orthogonally-triggered functions of the shape-memory were shown. Furthermore, a versatile approach to assemble stimuli-responsive DNA-based acrylamide hydrogel films on surfaces is presented. The method involves the activation of the hybridization chain-reaction (HCR) by a surface-confined promoter strand, in the presence of acrylamide chains modified with two DNA hairpin structures and appropriate stimuli-responsive tethers. The resulting hydrogel-modified surfaces revealed switchable stiffness properties and signal-triggered catalytic functions. By applying the method to assemble the hydrogel microparticles, substrate-loaded, stimuli-responsive microcapsules are prepared. The signal-triggered DNA-based hydrogel microcapsules are applied as drug carriers for controlled release. The different potential applications and future perspectives of stimuli responsive hydrogels are discussed. Specifically, the use of these smart materials and assemblies as carriers for controlled drug release and as shape-memory matrices for information storage and inscription and the use of surface-confined stimuli-responsive hydrogels, exhibiting switchable stiffness properties, for catalysis and controlled growth of cells are discussed.