We provide an overview of formal duality with an emphasis on the authors contributions. Every formally dual set can be obtained from a primitive formally dual set or, more generally from an irreducible formally dual set.Using several methods, including even set theory and the field-descent method, it is possible to obtain examples of primitive/irreducible formally dual sets as well as non-existence results. A graph search algorithm can be used for further investigation. Overall, primitive formally dual sets seem rare in cyclic groups, but occasionally exist in finite abelian groups.<eng>
