Studies of chromosome and genome biology often focus on condensed chromatin in the form of chromosomes and neglect the non-dividing cells. Even when interphase nuclei are considered, they are often then treated as interchangeable round objects. However, different cell types can have very different nuclear shapes, and these shapes have impacts on cellular function; indeed, many pathologies are linked with alterations to nuclear shape. In this review, we describe some of the nuclear morphologies beyond the spherical and ovoid. Many of the leukocytes of the immune system have lobed nuclei, which aid their flexibility and migration; smooth muscle cells have a spindle shaped nucleus, which must deform during muscle contractions; spermatozoa have highly condensed nuclei which adopt varied shapes, potentially associated with swimming efficiency. Nuclei are not passive passengers within the cell. There are clear effects of nuclear shape on the transcriptional activity of the cell. Recent work has shown that regulation of gene expression can be influenced by nuclear morphology, and that cells can drastically remodel their chromatin during differentiation. The link between the nucleoskeleton and the cytoskeleton at the nuclear envelope provides a mechanism for transmission of mechanical forces into the nucleus, directly affecting chromatin compaction and organisation.Leverhulme Trust (Grant ID: RPG337), Biotechnology and Biological Sciences Research Council (Grant IDs: BB/N000129/1, BB/L502443/1)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00412-016-0614-