Managing inventories, and thereby material flows, is of key importance for achieving efficient and sustainable supply chains. Green inventory management is characterized by complementing the traditional economic (cost) focus with environmental (emissions) considerations. In this chapter we identify and discuss key questions and challenges for green inventory management research. We do so by categorizing the costs and emissions of operating an inventory system into those associated with: ordering and transporting items, holding items in stock, and not satisfying customer demand on time. A literature overview illustrates what issues have been addressed so far in this emerging field. We conclude that there is a promising potential for green inventory management practices to reduce both costs and emissions, but much remains to be done. Not least in terms of developing more general green inventory models for practical use.