Multilinear subspace learning (MSL) aims to learn a specific small part of a large space of multidimensional objects having a particular desired property. It is a dimensionality reduction approach for finding a low-dimensional representation with certain preferred characteristics of high-dimensional tensor data through direct mapping, without going through vectorization. The term tensor in MSL refers to multidimensional arrays. Examples of tensor data include images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D). The mapping from a high-dimensional tensor space to a low-dimensional tensor space or vector space is named as multilinear projection. MSL methods are higher-order generalizations of linear subspace learning methods such as principal component analysis (PCA), linear discriminant analysis (LDA) and canonical correlation analysis (CCA). In the literature, MSL is also referred to as tensor subspace learning or tensor subspace analysis. Research on MSL has progressed from heuristic exploration in 2000s (decade) to systematic investigation in 2010s. … Multilinear Subspace Learning (MSL)