Real-time detection and identification of military and civilian targets from airborne platforms using hyperspectral sensors is of great interest. Relative to multispectral sensing, hyperspectral sensing can increase the detectability of pixel and subpixel size targets by exploiting finer detail in the spectral signatures of targets and natural backgrounds. A multitude of adaptive detection algorithms for resolved or subpixel targets, with known or unknown spectral characterization, in a background with known or unknown statistics, theoretically justified or ad hoc, with low or high computational complexity, have appeared in the literature or have found their way into software packages and end-user systems. The purpose of this paper is threefold. First, we present a unified mathematical treatment of most adaptive matched filter detectors using common notation, and we state clearly the underlying theoretical assumptions. Whenever possible, we express existing ad hoc algorithms as computationally simpler versions of optimal methods. Second, we assess the computational complexity of the various algorithms. Finally, we present a comparative performance analysis of the basic algorithms using theoretically obtained performance characteristics. We focus on algorithms characterized by theoretically desirable properties, practically desired features, or implementation simplicity. Sufficient detail is provided for others to verify and expand this evaluation and framework. A primary goal is to identify best-of-class algorithms for detailed performance evaluation.