This article is part (the 4 th article) of the themed issue (a monograph) “Aberrant cytogenetic and reproductive patterns in the evolution of Paraneoptera ”. The purpose of this article is to consider chromosome structure and evolution, chromosome numbers and sex chromosome systems, which all together constitute the chromosomal basis of reproduction and are essential for reproductive success. We are based on our own observations and literature data available for all major lineages of Paraneoptera including Zoraptera (angel insects), Copeognatha (= Psocoptera ; bark lice), Parasita (= Phthiraptera s. str; true lice), Thysanoptera (thrips), Homoptera (scale insects, aphids, jumping plant-lice, whiteflies, and true hoppers), Heteroptera (true bugs), and Coleorrhyncha (moss bugs). Terminology, nomenclature, classification, and the study methods are given in the first paper of the issue ( Gavrilov-Zimin et al. 2021).