Spermatogenesis is central to successful sexual reproduction, producing large numbers of haploid motile male gametes. Throughout this process, a series of equational and reductional chromosome segregation precedes radical repackaging of the haploid genome. Faithful chromosome segregation is thus crucial, as is an ordered spatio-temporal ‘dance’ of packing a large amount of chromatin into a very small space. Ergo, when the process goes wrong, this is associated with an improper chromosome number, nuclear position and/or chromatin damage in the sperm head. Generally, screening for overall DNA damage is relatively commonplace in clinics, but aneuploidy assessment is less so and nuclear organisation studies form the basis of academic research. Several studies have focussed on the role of chromosome segregation, nuclear organisation and analysis of sperm morphometry in human subfertility observing significant alterations in some cases, especially of the sex chromosomes. Importantly, sperm DNA damage has been associated with infertility and both extrinsic (e.g. lifestyle) and intrinsic (e.g. reactive oxygen species levels) factors, and while some DNA-strand breaks are repaired, unexpected breaks can cause differential chromatin packaging and further breakage. A ‘healthy’ sperm nucleus (with the right number of chromosomes, nuclear organisation and minimal DNA damage) is thus an essential part of reproduction. The purpose of this review is to summarise state of the art in the fields of sperm aneuploidy assessment, nuclear organisation and DNA damage studies.