Title: A Short History of Computational Complexity Author: Lance Fortnow, NEC Research and Steven Homer, BU Date: October 30, 2002 Abstract: A brief history of the major issues and developments in computational complexity theory over the past 30 years is presented. This paper will appear in the volume entitled, "A History of Mathematical Logic", edited by D. van Dalen, J. Dawson and A. Kanamori, and published by Elsevier.