<p>This thesis addresses two separate naturalness issues which generically come to bear on physical theories with large extra dimensions, and so a gravity scale much lower than the Planck scale. The first is related to the observed stability of the proton, wherein we determine the relevant constraints on an additional gauge boson which conserves baryon number. Although several such proposals have been previously considered, our analysis is distinctive in its interest in lighter gauge boson masses (which naturally arise in such models), and in its focus on the dependence of constraints due to kinetic mixing effects. The second is related to the main purpose of large extra dimensions---namely, to address the smallness of the observed vacuum energy---wherein we compute the leading-order quantum corrections to the four-dimensional (4D) vacuum energy resulting from loops of extra-dimensional fields. We compute the contributions from bulk scalars (spin 0), fermions (spin 1/2), and gauge fields (spin 1) in a flux-stabilized, spheroidal extra-dimensional geometry whose rugby-ball shape is due to two codimension-2 branes---one at each pole. (We also obtain the corresponding beta functions for both bulk and brane operators.) These results are then combined to obtain the net contribution from various multiplets in the context of a particular supersymmetric extra-dimensional model that has been shown to give a vanishing result for the 4D vacuum energy at the classical level. Surprisingly, we find that supersymmetry can be preserved dynamically at one loop in the case of identical branes, without arranging any particular relationship between the brane parameters. Perturbing away from the case of identical branes is shown to give a positive 1-loop contribution to the 4D vacuum energy whose size is set by the radius of the extra dimensions.</p> / Doctor of Philosophy (PhD)