DNA's programmable, predictable, and precise self-assembly properties enable structural DNA nanotechnology. DNA nanostructures have a wide range of applications in drug delivery, bioimaging, biosensing, and theranostics. However, physiological conditions, including low cationic ions and the presence of nucleases in biological systems, can limit the efficacy of DNA nanostructures. Several strategies for stabilizing DNA nanostructures have been developed, including i) coating them with biomolecules or polymers, ii) chemical cross-linking of the DNA strands, and iii) modifications of the nucleotides and nucleic acids backbone. These methods significantly enhance the structural stability of DNA nanostructures and thus enable in vivo and in vitro applications. This study reviews the present perspective on the distinctive properties of the DNA molecule and explains various DNA nanostructures, their advantages, and their disadvantages. We provide a brief overview of the biomedical applications of DNA nanostructures and comprehensively discuss possible approaches to improve their biostability. Finally, the shortcomings and challenges of the current biostability approaches are examined.