Feature selection has gained much consideration from scholars working in the domain of machine learning and data mining in recent years. Feature selection is a popular problem in Machine learning with the goal of finding optimal features with increase accuracy. As a result, several studies have been conducted on multi-objective feature selection through numerous multi-objective techniques and algorithms. The objective of this paper is to present a systematic literature review of the challenges and issues of the multi-objective feature selection problem and critically analyses the proposed techniques used to tackle this problem. The conducted review covered all related studies published since 2012 up to 2019. The outcomes of the reviewed of these studies clearly showed that no perfect solution to the multi-objective feature selection problem yet. The authors believed that the conducted review would serve as the main source of the techniques and methods used to resolve the problem of multi-objective feature selection. Furthermore, current challenges and issues are deliberated to find promising research domains for further study.