Inertia
Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertia and inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning (in fact, the entire theory was based on Newton's definition of inertia). However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to reference frames that were "inertial" in nature (meaning when no acceleration was present). In an attempt to address this limitation, Einstein proceeded to develop his general theory of relativity ("The Foundation of the General Theory of Relativity," 1916), which ultimately provided a unified theory for both "inertial" and "noninertial" (accelerated) reference frames. However, in order to accomplish this, in general relativity, Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton.
Spacetime
Other physicists and mathematicians at the turn of the century came close to arriving at what is currently known as spacetime. Einstein himself noted, that with so many people unraveling separate pieces of the puzzle, "the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905."
An important example is Henri Poincaré, who in 1898 argued that the simultaneity of two events is a matter of convention. In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by applying an explicitly "operational definition" of clock synchronization assuming constant light speed. In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity, and in 1905/1906 he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional space-time by defining various four vectors, namely four-position, four-velocity, and four-force. He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world". Furthermore, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform. For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity.