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The Method of Moments is one of a series of closely related transform methods which have been developed primarily for the deconvolution and analysis of fluorescence decay data. The main distinguishing feature of the Method of Moments is that it has been designed to be robust with respect to several important nonrandom errors of instrumental origin. The historical development of the method is reviewed here. Several new extensions are also described, including a statistical theory, an improved global analysis, and a method for analyzing continuous distributions of lifetimes. The new statistical theory is the first to incorporate a combined treatment of exponential depression and moment index displacement, both necessary components of the Method of Moments. In comparisons with the more commonly used least squares iterative reconvolution (LSIR) approach, it is shown that, in analyses of ideal synthetic data …