Acceptance of liver grafts from donations after circulatory death (DCD) largely remains a “black box,” particularly due to the unpredictability of the agonal phase. Abdominal normothermic regional perfusion (aNRP) can reverse ischemic injury early during the procurement procedure, and it simultaneously enables graft viability testing to unravel this black box. This review evaluates current protocols for liver viability assessment to decide upon acceptance or decline during aNRP. The Preferred Reporting Items for Systematic Reviews and Meta‐Analyses (PRISMA) guideline was used, and relevant literature databases were searched. The primary outcome consisted of criteria for liver graft viability assessment. Secondary outcomes included survival, primary nonfunction (PNF), early dysfunction, and biliary complications. A total of 14 articles were included in the analysis. In all protocols, a combination of criteria was used to assess suitability of the liver for transplantation. As many as 12 studies (86%) used macroscopic assessment, 12 studies (86%) used alanine transaminase (ALT) levels in perfusate, 9 studies (64%) used microscopic assessment, and 7 studies (50%) used lactate levels as assessment criteria. The organ utilization rate (OUR) was 16% for uncontrolled donation after circulatory death (uDCD) and 64% for controlled donation after circulatory death (cDCD). The most used acceptation criterion in uDCD is ALT level (31%), while in cDCD macroscopic aspect (48%) is most used. Regarding postoperative complications, PNF occurred in 13% (6%–25%) of uDCD livers and 3% (2%–4%) of cDCD livers. In uDCD, the 1‐year graft and patient survival rates were 75% (66%–82%) and 82% (75%–88%). In cDCD, the 1‐year graft and patient survival rates were 91% (89%–93%) and 93% (91%–94%), respectively. In conclusion, the currently used assessment criteria consist of macroscopic aspect and transaminase levels. The acceptance criteria should be tailored according to donor type to prevent an unacceptable PNF rate in uDCD and to increase the relatively modest OUR in cDCD.