Tensors (also known as multidimensional arrays or N-way arrays) provide powerful tools for data representation and analysis. Consequently, they have been used in a variety of sciences ranging from chemometrics to psychometrics and most recently to data mining. In this talk, I'll provide a brief tutorial on tensors and their decompositions, assuming only a background in linear algebra. I will then describe the MATLAB Tensor Toolbox for working with dense, sparse, and structured tensors. I'll conclude with examples from several data mining contexts including web mining and cross-language information retrieval. This is joint work with Brett Bader, Sandia National Labs.