Explore tensor decomposition as a powerful mathematical tool for data analysis in this SIAM Invited Address from the 2018 Joint Mathematics Meetings. Delve into the fundamentals of tensors, vector outer products, and matrix decomposition for detecting low-rank structures. Learn about CP tensor factorization and its applications in neuroscience and hazardous gas detection. Discover advanced techniques like Rayleigh CP with linear link, generalized CP, and Boolean CP for analyzing diverse datasets including mouse experiments and binary chat data. Gain insights into solving least squares problems and implementing alternating least squares for CP fitting.