Generalized decomposition models were developed in Psychology for multiway arrays having three or more dimensions (i.e., third- and higher-order tensors). Harshman (1970) and Car-roll (1970) independently proposed the trilinear model and called it, respectively, Parafac (Parallel factor analysis) and Candecomp (Canonical decomposition for three-way multidimensional model, Indscal). The Parafac/Candecomp model was actually a few years preceded by a more general model by Tucker (1964), called the Tucker model. Multiway arrays have distinctive mathematical properties than matrices. For example, I  J  K arrays can have maximum rank greater than max(I; J;K). This talk will introduce Parafac and Tucker models as well as several hybrid models. In addition, basic properties of tensors will be discussed. Parameters of tensor models are iteratively estimated by alternating least-squares (ALS) or its variants. Schematic principles of ALS will be mentioned. As examples, four applications of various models will be presented.