The search and the analysis of English scientific literature from 2005 to 2020 devoted to the methods of obtaining branched polymers and copolymers of N-isopropylacrylamide were made in order to obtain novel materials with valuable properties. It was found that modern methods of controlled radical polymerization were mainly used for this purpose, namely, atom transfer radical polymerization (ATRP), polymerization with reversible addition-fragmentation chain transfer (RAFT) and group transfer polymerization (GTP). In most cases the original compounds were the chain transfer agents in RAFT. CuCl was commonly used as a catalyst in ATRP; while in some cases cores of a different chemical nature (?-cyclodextrin, zinc phthalocyanine or zinc porphyrin) were used. In a number of cases, click chemistry reactions were used for synthesis. Depending on the order of the synthesis, a distinction was made between the “corearms” and “arms-core” approaches. The prospects of using branched N-isopropylacrylamide polymers as thermoresponsive materials, membranes for controlled drug release, photocatalysts, and agents of targeted photodynamic therapy and photoelectric storage of information were estimated.