Several exciting developments in the field of symplectic geometry took place in the years preceding this lecture. Researchers in this area began to make progress in solving many important and hitherto inaccessible problems. The techniques making this possible came both from the calculus of variations and from the theory of elliptic partial differential operators. McDuff examines some of these developments, including Gromov's results using elliptic methods, and how Floer applied these elliptic techniques to develop a new approach to Morse theory. In addition to researchers interested in this area, graduate students or advanced undergraduates find this lecture accessible.