Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind sources separation (BSS), especially multiway Independent Component Analysis (ICA), Nonnegative Matrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (SmoCA) and Sparse Component Analysis (SCA). Moreover, tensor decompositions have many other potential applications beyond multilinear BSS, especially feature extraction, classification, dimensionality reduction and multiway clustering. In this paper, we overview briefly promising models and approaches for tensor decompositions in applications to group and linked multiway BSS/ICA, feature extraction, classification and Multiway Partial Least Squares (MPLS) regression problems.