Whenever a new sensor or system comes online, engineers and analysts responsible for processing the measured data turn first to methods that are tried and true on existing systems. This is a natural, if not wholly logical approach, and is exactly what has happened in the advent of hyperspectral imagery (HSI) exploitation. However, a closer look at the assumptions made by the approaches published in the literature has not been undertaken. This thesis analyzes three key aspects of HSI exploitation: statistical data modeling, covariance estimation from training data, and dimension reduction. These items are part of standard processing schemes, and it is worthwhile to understand and quantify the impact that various assumptions for these items have on target detectability and detection statistics. First, the accuracy and applicability of the standard Gaussian (i.e., Normal) model is evaluated, and it is shown that the elliptically contoured t-distribution (EC-t) sometimes offers a better statistical model for HSI data. A finite mixture approach for EC-t is developed in which all parameters are estimated simultaneously without a priori information. Then the effects of making a poor covariance estimate are shown by including target samples in the training data. Multiple test cases with ground targets are explored. They show that the magnitude of the deleterious effect of covariance contamination on detection statistics depends on algorithm type and target signal characteristics. Next, the two most widely used dimension reduction approaches are tested. It is demonstrated that, in many cases, significant dimension reduction can be achieved with only a minor loss in detection performance. In addition, a concise development of key HSI detection algorithms is presented, and the state-of-the-art in adaptive detectors is benchmarked for land mine targets. Methods for detection and identification of airborne gases using hyperspectral imagery are discussed, and this application is highlighted as an excellent opportunity for future work.