Malignant tumours are often characterised by significant rearrangement of the genome. This may be visible in the form of a deranged karyotype with both loss and gain of DNA sequences extending from chromosomal regions to whole chromosomes. In several tumour types, however, gross genomic derangements are minimal, and tumour cells contain one or more additional (supernumerary) chromosomes that may be unrecognisable in terms of a single origin. In this review we term such chromosomes cancer-associated neochromosomes (CaNCs). In the absence of other identified genomic abnormalities, and because the CaNC is a common feature of the cancer type, it is hypothesised that the genetic alterations required for cell transformation are contained within its structure. In this review, we discuss the potential impact of modern genomic technologies on our understanding of the nature and causes of CaNC formation, which is central to several cancer types, exemplified here by well-differentiated liposarcoma.