Constraints on theories with large extra dimensions

Recently, a number of authors have challenged the conventional assumption t hat the string scale, Planck mass, and unification scale are roughly compar able. It has been suggested that the string scale could be as low as a TeV. In this note, we explore constraints on these scenarios. We argue that the most plausible cases have a fundamental scale of at least 10 TeV and five dimensions of inverse size 10 MeV. We show that a radial dilaton mass in th e range of proposed millimeter scale gravitational experiments arises natur ally in these scenarios. Most other scenarios require huge values of flux a nd may not be realizable in M Theory. Existing precision experiments put a conservative lower bound of 6 - 10 TeV on the fundamental energy scale. We note that large dimensions with bulk supersymmetry might be a natural frame work for quintessence, and make some other tentative remarks about cosmolog y.