This paper deals with some conceptual questions concerning physical constants, such as:

Why are there “fundamental constants” in physics and not, for instance, in biology or geology?

Why are there no such constants in the ancient theories of physics, such as classical mechanics?

Are all the modern physical constants on the same footing, whether they be masses of elementary particles, coupling constants, etc.?

Are classical constants such as R and J really less fundamental than modern constants, such as c and h?

Is there anything common between a simple unit conversion factor, such as the ratio of litre to cubic centimetre, and a universal constant, such as Planck’s?

Why is the velocity of light c considered as a universal constant when it seems to be specifically associated with the propagation of electromagnetic radiation?

What is the meaning of taking the values of some constants as unity, as though these values was not to be experimentally determined?

I will endeavour to show that the answers to these questions and other ones rely on the understanding of physical science as a historical process. Only by studying the conditions for the appearance, or disappearance, of physical constants can we understand their nature. Only by emphasizing the variations in status of a given constant can we understand its role. Only by contrasting the opposite effects of theoretical and experimental practices upon the fate of such a constant can we analyse its significance. The present investigation thus takes place within a definite vision of physics, and science in general, as a social endeavour. Its ensuing historicity should then be put into light, even at its seemingly most abstract and formal levels. The case of physical constants thus epitomizes this view, since their constant numerical values make sense only through a changing conceptual nature.