Abstract: The celebrated quadratic assignment problem (QAP) is an NP-hard, discrete, nonlinear optimization problem. Since its inception over 50 years ago, the QAP has received considerable attention from both practitioners and theoreticians alike, due to the diversity of its practical applications and its resistance to exact solution methods. This talk will provide general background information about the QAP, as well as an introduction to the three major avenues of current QAP research. No prior operations research or optimization knowledge will be assumed.