Nowadays, our society is facing problems related to energy availability. Owing to the energy savings that insulators provide, the search for effective insulating materials is a focus of interest. Since the current insulators do not meet the increasingly strict requirements, developing materials with a greater insulating capacity is needed. Until now, several nanoporous materials have been considered as superinsulators achieving thermal conductivities below that of the air 26 mW/(m K), like nanocellular PMMA/TPU, silica aerogels, and polyurethane aerogels reaching 24.8, 10, and 12 mW/(m K), respectively. In the search for the minimum thermal conductivity, still undiscovered, the first step is understanding heat transfer in nanoporous materials. The main features leading to superinsulation are low density, nanopores, and solid interruptions hindering the phonon transfer. The second crucial condition is obtaining reliable thermal conductivity measurement techniques. This review summarizes these techniques, and data in the literature regarding the structure and thermal conductivity of two nanoporous materials, nanocellular polymers and aerogels. The key conclusion of this analysis specifies that only steady-state methods provide a reliable value for thermal conductivity of superinsulators. Finally, a theoretical discussion is performed providing a detailed background to further explore the lower limit of superinsulation to develop more efficient materials.