Tumor cells typically contain a genome that is highly divergent from the genome of normal, non-transformed cells. This genetic divergence is caused by a number of distinct changes that the tumor cell acquires during its transformation from a normal cell into a tumorigenic counterpart. Changes to the genome include mutations, deletions, insertions, and also gross chromosomal aberrations, such as chromosome translocations and whole chromosome gains or losses. This genetic disorder of the tumor cell has complicated the identification of crucial driver mutations that cause cancer. Moreover, the large genetic divergence between different tumors causes them to behave very differently, and makes it difficult to predict response to therapy. In addition, tumor cells are genetically unstable and frequently acquire new mutations and/or gross chromosomal aberrations as they divide. This is beneficial for the overall capacity of a tumor to adapt to changes in its environment, but newly acquired genetic alterations can also compromise the genetic dominance of the tumor cell and thus affect tumor cell viability. Here, we review the mechanisms that can cause gross chromosomal aberrations, and discuss how these affect tumor cell viability.