In this letter, we introduce deep active learning (AL) for multi-label classification (MLC) problems in remote sensing (RS). In particular, we investigate the effectiveness of several AL query functions for MLC of RS images. Unlike the existing AL query functions (which are defined for single-label classification or semantic segmentation problems), each query function in this paper is based on the evaluation of two criteria: i) multi-label uncertainty; and ii) multi-label diversity. The multi-label uncertainty criterion is associated to the confidence of the deep neural networks (DNNs) in correctly assigning multi-labels to each image. To assess this criterion, we investigate three strategies: i) learning multi-label loss ordering; ii) measuring temporal discrepancy of multi-label predictions; and iii) measuring magnitude of approximated gradient embeddings. The multi-label diversity criterion is associated to the selection of a set of images that are as diverse as possible to each other that prevents redundancy among them. To assess this criterion, we exploit a clustering based strategy. We combine each of the above-mentioned uncertainty strategies with the clustering based diversity strategy, resulting in three different query functions. All the considered query functions are introduced for the first time in the framework of MLC problems in RS. Experimental results obtained on two benchmark archives show that these query functions result in the selection of a highly informative set of samples at each iteration of the AL process.