We review the framework, in which our world is a 3-brane floating in a flat, infinite-volume extra space, where high-dimensional gravity and possibly some other standard model gauge fields propagate. The brane fluctuations induce a four-dimensional Einstein term, which generates an effectively 4D gravity on the brane. In a similar way an effective 4D gauge theory is induced from the bulk gauge theory. These theories exhibit the phenomenon of an "infrared transparency", due to which the long wavelength modes penetrate easier in extra dimensions. This results in long distance astrophysical effects, such as dissipation of a long wavelength gravitational or electromagnetic radiation from distant sources into extra dimensions at an in-principle-observable rate. The framework also allows the supersymmetry to be unbroken in the extra space, while broken on the brane, which may shed a new light on the cosmological constant problem.