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The appearance of new fundamental forces and extra-dimensional modificationsto gravity in extensions of the Standard Model has motivated considerableinterest in testing Newtonian gravity at short distances (<10^-3 m). Presentlya number of new gravity experiments are searching for non-Newtonian effects inthe ranges 10^-4 m -- 10^-3 m. However, as challenging as these experimentsare, formidable new obstacles await the next generation of experiments whichwill probe gravity at distances <10^-4 m where Casimir/van der Waals forcesbecome dominant. Here we will review the motivation for conducting such veryshort distance gravity experiments, and discuss some of the new problems thatmay arise in future experiments. Finally, we suggest schematic designs for nullexperiments which would address some of these problems using the``iso-electronic'' and ``finite-size'' effects.Comment: 16 pages, 6 figures, LaTeX, (uses cite.sty), will appear in "Testing  General Relativity in Space: Gyroscopes, Clocks, and Interferometers," edited  by C. L\"ammerzahl, C. W. F. Everitt, F. W. Hehl (Springer-Verlag, 2000);  replaced with slight revision which adds an additional reference and updates  another referenc

Searching for Extra Dimensions and New String-Inspired Forces in the Casimir Regime