This lecture will describe recent developments in our efforts to develop low-molecular weight catalysts for asymmetric reactions. Over time, our view of asymmetry has ebbed and flowed, with foci on enantioselectivity, site-selectivity and chemoselectivity. In most of our current work, we are studying issues related to enantioselectivity as a prelude to extrapolation of catalysis concepts to more complex molecular frameworks wherein multiple stereochemical issues are presented within a singular substrate. Moreover, we continuously examine an interplay between screening of catalyst libraries and more hypothesis-driven experiments that emerge from screening results. Some of the mechanistic paradigms, and their associated ambiguities, will figure strongly in the lecture.