Polymer materials are increasingly used in all spheres of human activity. Today, it is difficult to imagine our life without the use of polymer products. Polymers have played a crucial role in the development of many industries and, of course, can be considered as one of the main drivers of technological progress. The research on the creation of new polymer materials that are obtained by modifying known polymers with various fillers, including nanomaterials, is widespread nowadays. In the foreseeable future, the time will come for modified polymer composites, when up to 75% of all things and materials that surround us will contain nano-additives. Due to their unique properties, these polymer compounds are in demand not only in industry and in everyday life, but also in medicine. One well-known nanomaterial is carbon nanotubes. The existing applications of nanotubes are almost limitless. Using them as modifying additives, it is possible to improve the properties of almost all known materials: polymers, alloys, plastics, rubbers, concretes, etc. In this review paper, the well-known polymer polypropylene and carbon nanotubes are selected as the main subjects of this study. This choice is due to their high demand in medicine, electronics, construction, etc.