Nowadays, many real-world applications of our daily life generate massive volume of streaming data at a higher speed than ever before, to name a few, Web clicking data streams, sensor network data and credit transaction streams. Contrary to traditional data mining using static datasets, there are several challenges for data stream mining, for instance, finite memory, one-pass and timely reaction. In this survey, we provide a comprehensive review of existing multi-label streams mining algorithms and categorize these methods based on different perspectives, which mainly focus on the multi-label data stream classification. We first briefly summarize existing multi-label and data stream classification algorithms and discuss their merits and demerits. Secondly, we identify mining constraints on classification for multi-label streaming data, and present a comprehensive study in algorithms for multi-label data stream classification. Finally, several challenges and open issues in multi-label data stream classification are discussed, which are worthwhile to be pursued by the researchers in the future. INDEX TERMS Data stream mining, multi-label data, multi-label classification.