Low-rank matrix structures can be exploited in many ways. We seek to generalize this concept to higher order tensors by generalizing the Singular Value Decomposition (HOSVD). Several ideas have been put forward, each proving to have certain advantages and disadvantages. Different tensor decompositions will be briefly discussed and the more recent approach of TT tensors will be introduced. The alternating least squares (ALS) algorithm will be presented as one of the most basic yet reliable tools in tensor optimization.