Hyperspectral imagery contains a wealth of information about the material content of remotely imaged scenes based on the unique spectral characteristics of the objects within them. This information is perturbed by spectral properties of the illumination, atmosphere, and environment, as previously described, and is further corrupted by sensor spectral response and system noise. Extracting information from hyperspectral data for any application requires consideration of all of these factors. While analytical methods can be unique to a particular remote sensing application, they generally share the overall challenge of needing to sort through the huge volume of data that hyperspectral imagery can represent to detect specific materials of interest, classify materials into groupings with similar spectral properties, or estimate specific physical properties based on their spectral characteristics. Whether such an analysis is performed in a fully automated fashion or with significant manual intervention, the ability to perform these primary analytical functions relies on suitable underlying models for the observed data, relative to the expected signal, background, and noise properties. It also requires numerical methods to aid in the extraction of pertinent and useful information from the volume of data. Such models and methods are explored in this chapter. The emphasis is on statistical and geometric models that have been widely employed across hyperspectral remote sensing applications, even if they originated from other fields such as communications, speech processing, and pattern recognition. Since numerical approaches for hyperspectral image classification and target detection are closely coupled with underlying statistical models, this chapter serves as a basis for the two chapters to follow that address these topics.