The role of structural genetic changes in human disease has received substantial attention in recent decades, but surprisingly little is known about numerical chromosomal abnormalities, even though they have been recognized since the days of Boveri as partaking in different cellular pathophysiological processes such as cancer and genomic disorders. The current knowledge of the genetic and epigenetic consequences of aneuploidy is reviewed herein, with a special focus on using mosaic genetic syndromes to study the DNA methylation footprints and expressional effects associated with whole-chromosomal gains. Recent progress in understanding the debated role of aneuploidy as a driver or passenger in malignant transformation, as well as how the cell responds to and regulates excess genetic material in experimental settings, is also discussed in detail.