High multiplicity scheduling problems arise naturally in contemporary production settings where manufacturers combine economies of scale with high product variety. Despite their frequent occurrence in practice, the complexity of high multiplicity problems – as opposed to classical, single multiplicity problems – is in many cases not well understood. In this paper, we discuss various concepts and results that enable a better understanding of the nature and complexity of high multiplicity scheduling problems. The paper extends the framework presented in brauneret al. [journal of combinatorial optimization (2005) vol. 9, pp. 313–323] for single machine, non-preemptive high multiplicity scheduling problems, to more general classes of problems.