This article presents a brief survey on some of the latest developments in the area of reliability-based design optimization of structural systems under stochastic excitation. The contributions are grouped into three main categories, namely, sequential optimization approaches, stochastic search based techniques, and schemes based on augmented reliability spaces. The different approaches are described and summarized. In addition, remarks are provided about their range of application, advantages, disadvantages, relevance, and potential research directions. The literature review indicates that computational aspects play a key role in the solution of this class of optimization problems. Besides, this overview suggests that methods for optimal design in stochastic structural dynamics are no longer restricted to academic-type of problems but they can be used as tools in a class of engineering design problems as well. •Recent advances for reliability-based optimization of structural systems under stochastic excitation are presented.•Underlying reliability models are high-dimensional.•Available approaches are compared in terms of their scope of applications.•Computational aspects play a key role in solving this type of problems.•Current methods can be used in a class of practical-type of problems.•Further research can lead to significant advancements in this area.