There continues to be an ongoing need for fair and equitable organ allocation. The Model for End-stage Liver Disease (MELD) score has evolved as a calculated framework to evaluate and allocate patients for liver transplantation objectively. The original MELD score has undergone multiple modifications as it is continuously scrutinized for its accuracy in objectively representing the clinical context of patients with liver disease. Several refinements and iterations of the score have been developed, including the widely accepted MELD-Na score. In addition, the most recent updated iteration, MELD 3.0, has been created. The MELD 3.0 calculator incorporates new variables such as patient sex and serum albumin levels and assigns new weights for serum sodium, bilirubin, international normalized ratio, and creatinine levels. It is anticipated that the use of MELD 3.0 scores will reduce overall waitlist mortality and enhance access for female liver transplant candidates. However, despite the emergence of the MELD score as one of the most objective measures for fair organ allocation, various countries and healthcare systems employ alternative methods for stratification and organ allocation. This review article highlights the origins of the MELD score, its iterations, the current MELD 3.0, and future directions for managing liver transplantation organ allocation.