Up to now, rubber materials have been used in a wide range of applications, from automotive parts to special-design engineering pieces, as well as in the pharmaceutical, food, electronics, and military industries, among others. Since the discovery of the vulcanization of natural rubber (NR) in 1838, the continuous demand for this material has intensified the quest for a synthetic substitute with similar properties. In this regard, synthetic polyisoprene rubber (IR) emerged as an attractive alternative. However, despite the efforts made, some properties of natural rubber have been difficult to match (i.e., superior mechanical properties) due not only to its high content of cis-1,4-polyisoprene but also because its structure is considered a naturally occurring nanocomposite. In this sense, cutting-edge research has proposed the synthesis of nanocomposites with synthetic rubber, obtaining the same properties as natural rubber. This review focuses on the synthesis, structure, and properties of natural and synthetic rubber, with a special interest in the synthesis of IR nanocomposites, giving the reader a comprehensive reference on how to achieve a mimic of NR.