Without fillers, rubber types such as silicone rubber exhibit poor mechanical, thermal, and electrical properties. Carbon black (CB) is traditionally used as a filler in the rubber matrix to improve its properties, but a high content (nearly 60 per hundred parts of rubber (phr)) is required. However, this high content of CB often alters the viscoelastic properties of the rubber composite. Thus, nowadays, nanofillers such as graphene (GE) and carbon nanotubes (CNTs) are used, which provide significant improvements to the properties of composites at as low as 2–3 phr. Nanofillers are classified as those fillers consisting of at least one dimension below 100 nanometers (nm). In the present review paper, nanofillers based on carbon nanomaterials such as GE, CNT, and CB are explored in terms of how they improve the properties of rubber composites. These nanofillers can significantly improve the properties of silicone rubber (SR) nanocomposites and have been useful for a wide range of applications, such as strain sensing. Therefore, carbon-nanofiller-reinforced SRs are reviewed here, along with advancements in this research area. The microstructures, defect densities, and crystal structures of different carbon nanofillers for SR nanocomposites are characterized, and their processing and dispersion are described. The dispersion of the rubber composites was reported through atomic force microscopy (AFM), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). The effect of these nanofillers on the mechanical (compressive modulus, tensile strength, fracture strain, Young’s modulus, glass transition), thermal (thermal conductivity), and electrical properties (electrical conductivity) of SR nanocomposites is also discussed. Finally, the application of the improved SR nanocomposites as strain sensors according to their filler structure and concentration is discussed. This detailed review clearly shows the dependency of SR nanocomposite properties on the characteristics of the carbon nanofillers.