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The Standard Model of particle physics and the theory of General Relativity(GR) currently provide a good description of almost all phenomena of particlephysics and gravitation that have received controlled experimental tests.However, the Standard Model contains many a priori variable parameters whosevalues, and whose apparent (near-)constancy, have yet to receive a convincingtheoretical explanation. At the same time, GR may now require to be extended oraltered at the largest length scales, to account for the recent apparentaccelerated cosmological expansion. In this introductory review I presenttheoretical aspects of the search for explanations of the values and possiblevariations of fundamental ``constants'', focusing on the possibility ofunification of interactions. I also relate cosmological variations tomodifications of gravity both locally and cosmologically.

Fundamental constants and their variability in theories of High Energy Physics