GenEst (a generalized estimator of mortality) is a suite of statistical models and software tools for generalized mortality estimation. It was specifically designed for estimating the number of bird and bat fatalities at solar and wind power facilities, but both the software (Dalthorp and others,2018) and the underlying statistical models are general enough to be useful in various situations to estimate the size of open populations when detection probabilities and search coverages are less than 1. In this report, we outline the statistical models and data structures underlying the estimator. The models are numerous, complex, and intricately interwoven. Discussion begins with broad, high-level overviews of the general models. The lower-level technical details are then gradually added. Broader and less technical discussions on the general context and applications of the models and the use of the software are available in the software user guide (Simonis and others, 2018), vignettes bundled with the software, and the help files within the software itself.