This article provides an overview of tensor decomposition, a powerful tool in signal processing and machine learning. Tensors, or multi-way arrays, are generalizations of matrices and have seen increasing application in recent years. The authors aim to bridge the gap between theory and practice by covering fundamental concepts, algorithms, and applications. Key topics include tensor rank and decomposition, factorization models, uniqueness, optimization algorithms, statistical performance, and applications such as source separation, collaborative filtering, and topic modeling. The article also discusses the challenges and differences between signal processing and machine learning perspectives on tensor decomposition, emphasizing the importance of understanding both areas for effective research and development.This article provides an overview of tensor decomposition, a powerful tool in signal processing and machine learning. Tensors, or multi-way arrays, are generalizations of matrices and have seen increasing application in recent years. The authors aim to bridge the gap between theory and practice by covering fundamental concepts, algorithms, and applications. Key topics include tensor rank and decomposition, factorization models, uniqueness, optimization algorithms, statistical performance, and applications such as source separation, collaborative filtering, and topic modeling. The article also discusses the challenges and differences between signal processing and machine learning perspectives on tensor decomposition, emphasizing the importance of understanding both areas for effective research and development.