Remanufacturing is an important product recovery option that benefits our sustainable development. Cores, i.e. the used products/parts, are essential resources for remanufacturing. Without cores, there will not be any remanufactured products. Challenges in the core acquisition process are mainly caused by the uncertainties of: return volume, timing and core quality. Core Acquisition Management actively attempts to reduce these uncertainties and achieve a better balance of demand and return for the remanufacturers. The aim of this dissertation is to extend the knowledge of Core Acquisition Management in remanufacturing, by investigating the current status of research and industrial practice, and developing quantitative models that assist the decision making in the core acquisition process. In the dissertation, a literature review is firstly conducted to provide an overview about the current research in Core Acquisition Management. Possible further research interests, for example, more studies based on non-hybrid remanufacturing systems and imperfect substitution assumption are suggested. Through an industrial survey carried out in a fast developing remanufacturing market - China, environmental responsibility and ethical  concerns, customer orientation and strategic advantage are identified as the most important motives for the remanufacturers, while customer recognition is their most serious barrier at present. Suggestions for further improving the Chinese remanufacturing industry from the policy-makers’ perspective are provided. After the above investigation, mathematical models are then developed to assist the acquisition decisions in two aspects: to deal with the uncertainties of return volume and timing, and to deal with the uncertainties of core quality. Acquisition decision about volume and timing is firstly studied from a product life cycle perspective, where the demands for remanufactured products and the core availability change over time. According to industrial observations, the remanufacturing cost decreases with respect to its core inventory. Using optimal control theory, core acquisition and remanufacturing decisions are derived to maximize the remanufacturer's profit. It is found that besides a simple bang-bang type control policy (either collecting as much as possible, or nothing), a special form of synchronizing policy (adjusting the core collection rate with demand rate) also exists. Furthermore, the acquisition decision depends greatly on the valuation of cores, and Real Option Valuation approaches are later used to capture the value of flexibility provided by owning cores when different aspects of remanufacturing environment are random. More specifically, the value of disposing a core earlier is investigated when the price of remanufactured product is uncertain, and the impact of the correlation between stochastic demand and return is also studied. To deal with the uncertainties of core quality, refund policies with different numbers of quality classes are studied. Under the assumption of uniformly distributed quality, analytical solutions for these refund policies are derived. Numerical examples indicate that the customers’ valuation of cores is an important factor influencing the return rates and the remanufacturer’s profit. Refund policies with a small number of quality classes could already bring major advantages. Credit refund policies (without deposits) are included for comparisons. In addition, within a game theory framework, the trade-off of two types of errors of the quality inspection in a deposit-refund policy is studied. The salvage values of different cores show great influences on the remanufacturer’s policy choices. The value of information transparency about the inspection errors are studied under different conditions. Interestingly, the customer may actually return more low quality cores when the inspection accuracy is improved.