We discuss how to consistently perform effective Lagrangian computations in
quantum gravity with branes in compact extra dimensions. A reparametrization
invariant and infrared finite result is obtained in a non trivial way. It is
crucial to properly account for brane fluctuations and to correctly identify
physical observables. Our results correct some confusing claims in the
literature. We discuss the implications of graviton loops on electroweak
precision observables and on the muon g-2 in models with large extra
dimensions. We model the leading effects, not controlled by effective field
theory, by introducing a hard momentum cut-off.Comment: 9 pages + 4 eps figures, JHEP style latex document. The paper is
composed by a theoretical part, followed (after page 21) by a
phenomenological part. v2: version published in JHEP, few typos corrected.
v3: few additional typos corrected in the Appendi