The presence of an abnormal chromosomal content is probably the most universally conserved hallmark of cancer cells. Predicted at the beginning of the 20th century as the origin of tumours, and extensively documented thereafter, genomic instability lies at the core of neoplastic development. Regardless of this classic model, the actual impact that deficient control of genomic integrity has on human health and particularly on cancer development only started to gain attention from the scientific community two decades ago. From a bird's eye view and with a cancer-oriented perspective, in this work we will try to cover some of the concepts obtained from recent research in genomic instability. The review will end up presenting suggestive evidence which proposes that genomic instability might turn out to be not just the driving force but also the Achilles' heel of cancer.