The evolution of physics did not come to an end in the dawn of the 20th century, as many physicists believed at that time and as school textbooks seem to imply sometimes. Simply, the new avenue opened by Galilean transformations had come to an end at the moment when Lorentz transformations were introduced. Experimental results accumulated in the early 20th century, that could not be included in the edifice created along the way, gave rise to new questions and problems, which required a new approach to physics. The change in mainstream physics took place through the establishment of two novel theories: quantum mechanics and theory of relativity. What were, however, these new questions and problems? Their knowledge allows us to appreciate better the revolutionary and, at the same time, effective nature of both these new theories.