In the last decades, design optimization of structures received significant attention to reconcile economic aspects, after the recent advances in computer technology. Many solution methods have been developed in order to solve different kinds of optimization problems defined for design of structures. Concerning various types of structural loads, earthquake loading is a crucial factor influencing structural design. The procedures for analysis and design of structures to resist seismic excitations are in a progressive state of development, for which numerous optimization problems have been proposed. This article presents an overview of seismic design optimization of structures, focusing on common solution methods, types of optimization problem and goals of optimization. Past and recent developments are reviewed, and current gaps as well as some open concerns deserving more research in future studies are discussed.