Multi-label classification has gained in importance in the last decade and it is today confronted to the current needs to process massive raw data from heterogeneous sources. Therefore, dimensionality reduction, which aims at reducing the number of features, labels, or both, knows a renewed interest to enhance the scaling properties of the classifiers and their predictive performances. In this paper we review more than fifty papers presenting dimensionality reduction approaches for multi-label classification and we propose an analysis in three steps : (i) a typology of the methods describing the main components of their strategies, the problem they tackle and the way they solve it (ii) a unified formalization of the problems to help to distinguish the similarities and differences between the approaches, and (iii) a meta-analysis of the published experimental results inspired by the consensus theory to identify the most efficient algorithms.