Exabytes of data are generated daily by humans, leading to the growing needs for new efforts in dealing with the grand challenges for multi-label learning brought by big data. For example, extreme multi-label classification is an active and rapidly growing research area that deals with classification tasks with extremely large number of classes or labels; utilizing massive data with limited supervision to build a multi-label classification model becomes valuable for practical applications, etc. Besides these, there are tremendous efforts on how to harvest the strong learning capability of deep learning to better capture the label dependencies in multi-label learning, which is the key for deep learning to address real-world classification tasks. However, it is noted that there have been a lack of systemic studies that focus explicitly on analyzing the emerging trends and new challenges of multi-label learning in the era of big data. It is imperative to call for a comprehensive survey to fulfil this mission and delineate future research directions and new applications.