This is a brief summary and exposition of the paper "Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition," which was presented at the Second GI Conference on Automata Theory and Formal Languages, University of Kaiserslautern, May 1975, and which appears in the proceedings of that conference, Lecture Notes in Computer Science, Vol. 33 (Springer Verlag, Berlin, 1975, pages 134--183). A preliminary version of this paper was presented at the EUROSAM 74 Conference, Stockholm, July 1974, and appears in the proceedings of that conference, SIGSAM Bulletin, Vol. 8, No. 3 (August 1974), pages 30--90. The final version of the paper includes a rather detailed analysis of the computing time of the algorithm, which was omitted from the preliminary version In addition, the final version describes several significant improvements to the algorithm of the earlier version.