Multi-objective programming is commonly used in the literature when conflicted objectives arise in solving optimization problems. Over the past decades, classical optimization methods have been developed as useful tools to discover optimal solutions for multi-objective problems (MOPs). In recent years, under uncertainty, multi-objective Optimization (MOO) has received much attention due to its practical applications in real-world problems. However, many studies have been conducted on this matter. Some of which ignored the effects of uncertainty on optimization problems. This paper systematically reviews and summarizes various multi-objective methods applied to the problems with more than one objective in uncertain environments where uncertainty is expressed using fuzzy sets. In this paper, 439 articles on fuzzy multi-objective programming published from 1978 to 2021 are reviewed using corresponding texts, charts, and tables. Finally, the basic features of MOO are briefly presented, along with a prologue of MOO techniques and current trends. Recommendations for further research are also is provided.