Abstract: Let G be a group of order n. An External Difference Family (EDF) is a combinatorial structure formed by disjoint subsets of G, such that each element within G occurs exactly lambda times as a difference between elements of disjoint subsets. A Strong External Difference Family (SEDF) is an EDF with extra constraints on the number of times each element can occur as a difference between particular subsets. In this talk, I will fully introduce both of these combinatorial structures and discuss what we can say about the structure of EDFs, SEDFs and related combinatorial families, with particular focus on cyclotomic constructions within finite fields.