Micronuclei (MN) and other nuclear anomalies such as nucleoplasmic bridges (NPBs) and nuclear buds (NBUDs) are biomarkers of genotoxic events and chromosomal instability. These genome damage events can be measured simultaneously in the cytokinesis-block micronucleus cytome (CBMNcyt) assay. The molecular mechanisms leading to these events have been investigated over the past two decades using molecular probes and genetically engineered cells. In this brief review, we summarise the wealth of knowledge currently available that best explains the formation of these important nuclear anomalies that are commonly seen in cancer and are indicative of genome damage events that could increase the risk of developmental and degenerative diseases. MN can originate during anaphase from lagging acentric chromosome or chromatid fragments caused by misrepair of DNA breaks or unrepaired DNA breaks. Malsegregation of whole chromosomes at anaphase may also lead to MN formation as a result of hypomethylation of repeat sequences in centromeric and pericentromeric DNA, defects in kinetochore proteins or assembly, dysfunctional spindle and defective anaphase checkpoint genes. NPB originate from dicentric chromosomes, which may occur due to misrepair of DNA breaks, telomere end fusions, and could also be observed when defective separation of sister chromatids at anaphase occurs due to failure of decatenation. NBUD represent the process of elimination of amplified DNA, DNA repair complexes and possibly excess chromosomes from aneuploid cells.