The empirical Gramian framework -- emgr -- is a numerical software toolbox for the approximate computation of system-theoretic operators, the so-called system Gramians, which characterize input-output systems, the object of interest in mathematical system theory. Due to their data-driven computation, the empirical system Gramians happen to be compatible with a wide range of systems and facilitate various scientific and engineering applications. While this numerical software package is topically focused, the observations and experiences made during its more than eight years of continued advancement also relate to mathematical software in general, and encompass scientific and technical aspects of development and dissemination. In this contribution, these findings are classified and summarized from a mathematical and software perspective.