Copy number alterations (CNAs), resulting from the gain or loss of genetic material from as little as 50 base pairs or as big as entire chromosome(s), have been associated with many congenital diseases, de novo syndromes and cancer. It is established that CNAs disturb the dosage of genomic regions including enhancers/promoters, long non-coding RNA and gene(s) among others, ultimately leading to an altered balance of key cellular functions. In cancer, CNAs have been associated with almost all steps of the disease: predisposition, initiation, development, maintenance, response to treatment, resistance, and relapse. Therefore, understanding how specific CNAs contribute to tumourigenesis may provide prognostic insight and ultimately lead to the development of new therapeutic approaches to improve patient outcomes. In this review, we provide a snapshot of what is currently known about CNAs and cancer, incorporating topics regarding their detection, clinical impact, origin, and nature, and discuss the integration of innovative genetic engineering strategies, to highlight the potential for targeting CNAs using novel, dosage-sensitive and less toxic therapies for CNA-driven cancer.