Living donor kidney transplantation is the preferred treatment for patients suffering from end-stage renal disease. To alleviate the shortage of kidney donors, many advances have been made to improve the utilization of living donors deemed incompatible with their intended recipient. The most prominent of these advances is kidney paired donation (KPD), which matches incompatible patient-donor pairs to facilitate a kidney exchange. This review discusses the various approaches to matching and allocation in KPD. In particular, it focuses on the underlying principles of matching and allocation approaches, the combination of KPD with other strategies such as ABO incompatible transplantation, the organization of KPD, and important future challenges. As the transplant community strives to balance quantity and equity of transplants to achieve the best possible outcomes, determining the right long-term allocation strategy becomes increasingly important. In this light, challenges include making full use of the various modalities that are now available through integrated and optimized matching software, encouragement of transplant centers to fully participate, improving transplant rates by focusing on the expected long-run number of transplants, and selecting uniform allocation criteria to facilitate international pools.