In this chapter, we recall several classical results on positive operator semigroups on \(\textit{AL}\) -spaces, with a particular emphasis on perturbation settings. Special attention is given to peripheral spectral properties, which are central to the asymptotic analysis of such semigroups. We also present two fundamental generation theorems: Desch’s perturbation theorem and the Kato–Voigt perturbation theorem, the latter accompanied by its associated honesty theory.