Relief distribution is one of the most widely studied topics in the domain of emergency logistics. Optimization models and solving approaches have become one of the most powerful tools for tackling relief distribution problems. In this context, victims’ satisfaction should be considered as one significant indicator to evaluate relief distribution operations. Therefore, this survey addresses some of the most representative publications working with optimization models and solving approaches in relief distribution concerning victims’ satisfaction. Firstly, collected models are discussed from the commonly used objectives for describing victims’ satisfaction: the shortest distribution time, the lowest unmet demand, and the maximum fairness. Second, gathered solving approaches are analyzed from exact algorithms, heuristic algorithms, and machine learning algorithms respectively. Heuristic algorithms are further studied into four groups: genetic algorithm, ant colony optimization, particle swarm optimization, and others. Finally, development trends of models and approaches in relief distribution concerning victims’ satisfaction and potential interest in the cross-disciplinary are showcased.