According to scientific research from different countries, crumb rubber obtained from end-of-life tires (ELT) during processing can improve the properties of the asphalt mixture, thereby extending the service life of the road surface. This paper resents the modification of bitumen with industrial rubber waste. The modification of bitumen for roads is considered one of the most suitable and popular approaches. This research paper describes the details of using different types of crumb rubber as bitumen modifiers. The modified bitumen’s main physical and mechanical characteristics were determined after conventional tests: penetration and ductility, softening point, and Fraas brittleness point. In order to obtain a rubber–asphalt concrete mixture with improved performance characteristics, the viscoelastic and rheological properties of rubber–bitumen binders and their comparison with polymer–bitumen binders were also studied. The research results show that with increasing temperature, the values of viscosity, shear stress and complex shear modulus of all studied bitumen systems decrease, the values of the phase shift angle increase, and the size of the rubber particles has a greater influence on the properties of bitumen systems.