Tensor, or multiarrays with $d>=3$ indices, are ubiquitous in modern applications, mainly due to data explosion. While matrices, $d=2$, are well understood and widely used, tensors pose theoretical and numerical challenges. Tensors also arise naturally in quantum physics, when dealing with d-particle systems. In this talk, for general mathematical audience, we will describe several fundamental results and problems in tensors: tensor ranks, low rank approximation of tensors, spectral and nuclear norm of tensors, and their relation to the entanglement and nonseparability in quantum information theory.