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In this paper, we survey constructions of and nonexistence results oncombinatorial/geometric structures which arise from unions of cyclotomicclasses of finite fields. In particular, we survey both classical and recentresults on difference sets related to cyclotomy, and cyclotomic constructionsof sequences with low correlation. We also give an extensive survey of recentresults on constructions of strongly regular Cayley graphs and relatedgeometric substructures such as $m$-ovoids and $i$-tight sets in classicalpolar spaces.

Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs, and related geometric substructures