Time variation of constants of nature is still a question of debate among astronomers, physicists, geologists, and palaeontologists. But are the fundamental physical constants really varying in space or time and how changing these parameters may occur?. Paul Dirac was interested in this question in the large number hypothesis (LNH). He arrived by coincidence at the revolutionary hypothesis that the gravitational constant G should be varied inversely with the cosmic time t. LNH sparked off many ideas and arguments about the possibility of time or space variations of the fundamental constants of nature. In this work, we review details and arguments regarding the time and space variation of dimensional and dimensionless constants based on a detailed comparison for the recorded literature over about one and a half-century.