The concept of a spacetime coordinate system was introduced in 1907, two years after Einstein originally proposed the theory of special relativity. Hermann Minkowski, a former professor of Einstein, presented the idea of this spacetime coordinate system. The ideas were inherent in Einstein's version of the theory, but he hadn't thought of it that way. In a 1908 talk called "Space and Time," Minkowski elaborated on these concepts and they began to gain popularity.
In modern cosmology, it's possible for spacetime to expand. Einstein noticed this in his original equations for general relativity, but thought that expanding space made no sense, so he put in a correction called the cosmological constant. Years later, Edwin Hubble discovered that space was actually expanding. The modern theory of inflation actually indicates that space was once accelerating faster than the speed of light ... nothing in space can move faster than the speed of light, but space itself can move faster.