The number of patients placed on kidney transplant waiting lists is rapidly increasing, resulting in a growing gap between organ demand and the availability of kidneys for transplantation. This organ shortage has forced medical professionals to utilize marginal kidneys from expanded criteria donors (ECD) to broaden the donor pool and shorten wait times for patients with end-stage renal disease. However, recipients of ECD kidney grafts tend to have worse outcomes compared to those receiving organs from standard criteria donors (SCD), specifically increased risks of delayed graft function (DGF) and primary nonfunction incidence. Thus, representative methods for graft-quality assessment are strongly needed, especially for ECDs. Currently, graft-quality evaluation is limited to interpreting the donor’s recent laboratory tests, clinical risk scores, the visual evaluation of the organ, and, in some cases, a biopsy and perfusion parameters. The last few years have seen the emergence of many new technologies designed to examine organ function, including new imaging techniques, transcriptomics, genomics, proteomics, metabolomics, lipidomics, and new solutions in organ perfusion, which has enabled a deeper understanding of the complex mechanisms associated with ischemia-reperfusion injury (IRI), inflammatory process, and graft rejection. This review summarizes and assesses the strengths and weaknesses of current conventional diagnostic methods and a wide range of new potential strategies (from the last five years) with respect to donor graft-quality assessment, the identification of IRI, perfusion control, and the prediction of DGF.