  The elementary particles of the Standard Model may live in more than 3+1
dimensions. We study the consequences of large compactified dimensions on
scattering and decay observables at high-energy colliders. Our analysis
includes global fits to electroweak precision data, indirect tests at
high-energy electron-positron colliders (LEP2 and NLC), and direct probes of
the Kaluza-Klein resonances at hadron colliders (Tevatron and LHC). The present
limits depend sensitively on the Higgs sector, both the mass of the Higgs boson
and how many dimensions it feels. If the Higgs boson is trapped on a 3+1
dimensional wall with the fermions, large Higgs masses (up to 500 GeV) and
relatively light Kaluza-Klein mass scales (less than 4 TeV) can provide a good
fit to precision data. That is, a light Higgs boson is not necessary to fit the
electroweak precision data, as it is in the Standard Model. If the Higgs boson
propagates in higher dimensions, precision data prefer a light Higgs boson
(less than 260 GeV), and a higher compactification scale (greater than 3.8
TeV). Future colliders can probe much larger scales. For example, a 1.5 TeV
electron-positron linear collider can indirectly discover Kaluza-Klein
excitations up to 31 TeV if 500 fb^-1 integrated luminosity is obtained.
