The nucleus is arguably the defining characteristic of eukaryotes, distinguishing their cell organisation from both bacteria and archaea. Though the evolutionary history of the nucleus remains the subject of debate, its emergence differs from several other eukaryotic organelles in that it appears not to have evolved through symbiosis, but by cell membrane elaboration from an archaeal ancestor. Evolution of the nucleus has been accompanied by elaboration of nuclear structures that are intimately linked with most aspects of nuclear genome function, including chromosome organisation, DNA maintenance, replication and segregation, and gene expression controls. Here we discuss the complexity of the nucleus and its substructures in protozoan eukaryotes, with a particular emphasis on divergent aspects in eukaryotic parasites, which shed light on nuclear function throughout eukaryotes and reveal specialisations that underpin pathogen biology.