Matrix decompositions have always been at the heart of signal, circuit and system theory. In particular, the Singular Value Decomposition (SVD) has been an important tool. There is currently a shift of paradigm in the algebraic foundations of these fields. Quite recently, Nonnegative Matrix Factorization (NMF) has been shown to outperform SVD at a number of tasks. Increasing research efforts are spent on the study and application of decompositions of higher-order tensors or multi-way arrays. This paper is a partial survey on tensor generalizations of the SVD and their applications. We also touch on Nonnegative Tensor Factorizations. A Survey of Tensor Methods