The first idea of extra dimensions, as it is well known, was proposed by Kaluza-Klein in the 1920's to unify electromagnetism and gravity. Since then, dimensional expansion of space-time beyond 4D has been one of the most interesting topics of Modern Physics. Besides extending of Standard Model (SM), introducing extra dimensions have been considered as the ways to investigate both classical and open problems of Particle physics and Cosmology in New Physics beyond the SM . These are solutions of the hierarchy problem in the 5D Randall-Sundrum space-time or in higher extra dimensions; the explanation of dark matter or dark energy, neutrino physics in the 6D Universal Extra Dimensions (UED) model, the expective proposal for Grand Unified Theory (GUT) base on String theories with 10D or 11D to unify gravity with gauge interactions. Extra dimensional theories can lead to really significant physical consequences.