Core acquisition is essential for the success of remanufacturing business. To describe the current status of the quantitative research in Core Acquisition Management and to indicate possible future research directions, a literature review is conducted in this paper about the quantitative modeling in Core Acquisition Management research area. The activities included in Core Acquisition Management are categorized into topics such as acquisition control, forecasting return, return strategies, quality classification and reverse channel design. While most of the studies focus on acquisition control, studies on return strategies and return forecast are relatively limited. Furthermore, this paper analyzes the research papers according to the key assumptions such as, hybrid/non-hybrid remanufacturing systems, acquisition functions, quality classification methods and perfect/imperfect substitutions. In conclusion, studies based on the assumptions of non-hybrid remanufacturing systems and imperfect substitution should gain more attentions, since these situations frequently occur in practice but are less investigated in the existing literature. In addition, empirical validation of the various forms of the acquisition function (relations between acquisition incentives and acquisition volume) should be important for further investigations.