The lack of an appropriate intracellular delivery system for therapeutic nucleic acids (TNAs) is a major problem in molecular biology, biotechnology, and medicine. A relatively new class of highly symmetrical hyperbranched polymers, called dendrimers, shows promise for transporting small TNAs into both cells and target tissues. Dendrimers have intrinsic advantages for this purpose: their physico-chemical and biological properties can be controlled during synthesis, and they are able to transport large numbers of TNA molecules that can specifically suppress the expression of single or multiple targeted genes. Numerous chemical modifications of dendrimers extend the biocompatibility of synthetic materials and allow targeted vectors to be designed for particular therapeutic purposes. This review summarizes the latest experimental data and trends in the medical application of various types of dendrimers and dendrimer-based nanoconstructions as delivery systems for short small interfering RNAs (siRNAs) and microRNAs at the cell and organism levels. It provides an overview of the structural features of dendrimers, indicating their advantages over other types of TNA transporters.