In generic string compactifications with branes, the regions of space in the vicinity of brane horizons, or brane throats, support effective potential barriers. raised by the background gravitational fields. A familiar example is the AdS brane throats in the Randall-Sundrum model. The barriers obstruct the interaction of observers inside different throats, whose communication is effectively described by tunneling through the barriers. Consequently the interactions between different throats are exponentially weak, This provides for a new mechanism for explaining small numbers in Nature. We review the applications to the hierarchy problem where supersymmetry breaking scale is reduced by tunneling, long-lived cold dark matter particles which decay into hot CFT, and consider the implications for holography. We finally discuss the important interplay between the tunneling suppression and our recent conjecture that blaholes stuck on a brane in AdS D + 1 should be interpreted as duals of quantum-corrected D-dimensional black holes. rather than classical ones, of a CFT coupled to gravity.