The Principal Component Decomposition (POD) technique has been used as a model reduction tool for many applications in engineering and science. In principle, one begins with an ensemble of data, called snapshots, collected from an experiment or laboratory results. The beauty of the POD technique is, when it is applied, the entire data set can be represented by the smallest number orthogonal basis elements. It is such capability that allows us to reduce the complexity and dimensions of many physical applications. Mathematical formulations and numerical schemes for the POD method will be discussed along with three applications, satellite photo image reconstruction, cancer detection with DNA microarrays, and stock allocation optimization.