Multi-label classification addresses the issues that more than one class label assigns to each instance. Many real-world multi-label classification tasks are high-dimensional due to digital technologies, leading to reduced performance of traditional multi-label classifiers. Feature selection is a common and successful approach to tackling this problem by retaining relevant features and eliminating redundant ones to reduce dimensionality. There is several feature selection that is successfully applied in multi-label learning. Most of those features are wrapper methods that employ a multi-label classifier in their processes. They run a classifier in each step, which requires a high computational cost, and thus they suffer from scalability issues. Filter methods are introduced to evaluate the feature subsets using information-theoretic mechanisms instead of running classifiers to deal with this issue. Most of the existing researches and review papers dealing with feature selection in single-label data. While, recently multi-label classification has a wide range of real-world applications such as image classification, emotion analysis, text mining, and bioinformatics. Moreover, researchers have recently focused on applying swarm intelligence methods in selecting prominent features of multi-label data. To the best of our knowledge, there is no review paper that reviews swarm intelligence-based methods for multi-label feature selection. Thus, in this paper, we provide a comprehensive review of different swarm intelligence and evolutionary computing methods of feature selection presented for multi-label classification tasks. To this end, in this review, we have investigated most of the well-known and state-of-the-art methods and categorize them based on different perspectives. We then provided the main characteristics of the existing multi-label feature selection techniques and compared them analytically. We also introduce benchmarks, evaluation measures, and standard datasets to facilitate research in this field. Moreover, we performed some experiments to compare existing works, and at the end of this survey, some challenges, issues, and open problems of this field are introduced to be considered by researchers in the future.