This chapter serves as an introduction to the monograph. It presents an overview of various integro-differential equations encountered in kinetic theory, mathematical biology, and other related fields, which motivated the systematic study undertaken in this monograph. These equations appear as jump perturbations of semiflows and, as such, share a suitable additive perturbation structure, allowing for a unified treatment by weak compactness methods in L1 spaces and the peripheral spectral theory of positive operators on Banach lattices. A brief overview of the different chapters is provided to facilitate reading the monograph.