Disaster recovery is widely regarded as the least understood phase of the disaster cycle. In particular, the literature around lifeline infrastructure restoration modeling frequently mentions the lack of empirical quantitative data available. Despite limitations, there is a growing body of research on modeling lifeline infrastructure restoration, often developed using empirical quantitative data. This study reviews this body of literature and identifies the data collection and usage patterns present across modeling approaches to inform future efforts using empirical quantitative data. We classify the modeling approaches into simulation, optimization, and statistical modeling. The number of publications in this domain has increased over time with the most rapid growth of statistical modeling. Electricity infrastructure restoration is most frequently modeled, followed by the restoration of multiple infrastructures, water infrastructure, and transportation infrastructure. Interdependency between multiple infrastructures is increasingly considered in recent literature. Researchers gather the data from a variety of sources, including collaborations with utility companies, national databases, and post-event damage and restoration reports. This study provides discussion and recommendations around data usage practices within the lifeline restoration modeling field. Following the recommendations would facilitate the development of a community of practice around restoration modeling and provide greater opportunities for future data sharing.