Tensor decompositions are structured representations of tensors that render them more amenable to storage, manipulation, and/or analysis. The alternating least squares (ALS/AltLS) method is a widely used algorithm for computing a tensor decomposition known as the CP decomposition; however, its convergence theory is still incompletely understood. In this talk, we will present joint work with Iwen, Needell, and Wang on local convergence theorems for CP-AltLS. In contrast to existing results, our analysis is more general, quantitative, explicit, and direct. No prior knowledge of tensor decompositions will be assumed.