The Special Theory of Relativity was developed at the end of the nineteenth century and the beginning of the twentieth century. It entirely replaced older physical theories such as Newtonian Physics and led to early Quantum Theory and General Relativity.
Special Relativity begins by re-examining the basis of Newtonian Physics and demonstrating that the Newtonian treatment of relative motion is incorrect. As a result the whole of classical physics must be rebuilt to account for this error.
Special Relativity does not just apply to fast moving objects, it affects the everyday world directly through "relativistic" effects such as magnetism and the relativistic inertia that underlies kinetic energy and hence the whole of dynamics.
Special Relativity is now one of the foundation blocks of physics. It is in no sense a provisional theory and is largely compatible with quantum theory; it not only led to the idea of matter waves but is the origin of 'spin' and underlies the existence of the antiparticles. Contrary to popular belief modern Special Relativity is not invalidated by effects such as quantum entanglement but rather provides the understanding of space and time through which these effects might be understood.