With a steep increase of the global disaster relief efforts around the world, the relief supply chain and humanitarian logistics play an important role to address this issue. A broad overview of operations research ranges from a principle or conceptual framework to analytical methodology and case study applied in this field. In this paper, we provide an overview of this challenging research area with emphasis on the corresponding optimization problems. The scope of this study begins with classification by the stage of the disaster lifecycle system. The characteristics of each optimization problem for the disaster supply chain are considered in detail as well as the logistics features. We found that the papers related to disaster relief can be grouped in three aspects in terms of logistics attributes: facility location, distribution model, and inventory model. Furthermore, the literature also analyzes objectives and solution algorithms proposed in each optimization model in order to discover insights, research gaps and findings. Finally, we offer future research directions based on our findings from the investigation of literature review.