Genomic instability is a driving force in the natural history of blood cancers including multiple myeloma,an incurable neoplasm of immunoglobulin producing plasma cells that reside in the hematopoietic bone marrow. Long recognized manifestations of genomic instability in myeloma at the cytogenetic level include abnormal chromosome numbers (aneuploidy) caused by trisomy of odd-numbered chromosomes; recurrent oncogene-activating chromosomal translocations that involve immunoglobulin loci; and large-scale amplifications, inversions, and insertions / deletions (indels). Catastrophic genetic rearrangements that either shatter and illegitimately reassemble a single chromosome (chromotripsis) or lead to disordered segmental rearrangements of multiple chromosomes (chromoplexy) also occur. Genomic instability at the nucleotide level results in base substitution mutations and small indels that affect both the coding and non-coding genome. Distinctive signatures of somatic mutations that can be attributed to defects in DNA repair pathways, the DNA damage response or aberrant activity of mutator genes including members of the APOBEC family have been identified. Here we review recent findings on genomic stability control in myeloma that are not only relevant for myeloma development and progression, but also underpin disease relapse and acquisition of drug resistance in patients with myeloma.