47 pps. 7/24/98 (Revised 10/17/99) Published in: "From Mechanics to Computation (Essays in Honor of Juan-Carlos Simo)," J. Nonlinear Sci. Editors (Springer, New York), 271--316 (2000). This paper is a revised and updated version of the review article ``Obstruction Results in Quantization Theory,'' which was published in J. Nonlinear Sci. 6, 469--498 (1996).