Readers of SIAM Review are always happy to learn about difficult and important real-world problems that can be modeled mathematically and solved numerically. And we are even happier when serious mathematical issues arise during the modeling, when the latest numerical methods are needed to solve the problem, and when the modeling and solution techniques lead to new research directions in mathematics, algorithms, and the associated applications areas. All of these properties are present in this issue's SIGEST paper, "Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions," by A. Ben-Tal, M. Kocvara, A. Nemirovski, and J. Zowe, which originally appeared in SIAM Journal on Optimization, volume 9, September 1999. This paper is informative on several levels. The authors begin with a highly readable overview of free material design problems in structural engineering and then discuss how to formulate the very difficult multiload problem, which turns out to require new mathematical and computational approaches. A crucial element is that calculation of the optimal elasticity matrix can be reduced to a semidefinite programming problem---optimization of an affine function of an (unknown) symmetric matrix subject to linear and positive-semidefiniteness constraints. Finally, the paper describes the success of semidefinite programming in solving three structural design problems. The appearance of semidefinite programming (SDP) in this paper is striking. Although the mathematical roots of SDP go back to the sixties, it has dramatically come to the fore only within the last few years---for example, it was the single most popular topic at both the 1999 SIAM Conference on Optimization and the 2000 International Symposium on Mathematical Programming. The analysis in this SIGEST paper illustrates one of the earliest applications of SDP, to structural optimization; SDP is also the foundation of much recent work on approximation algorithms for NP-hard combinatorial optimization problems. Every indication is that SDP will continue to grow as both theoretical paradigm and solution technique.