Aberrant chromosomal architecture, ranging from small insertions or deletions to large chromosomal alterations, is one of the most common characteristics of cancer genomes. Chromosomal instability (CIN) underpins much of the intratumoural heterogeneity observed in cancers and drives phenotypic adaptation during tumour evolution. Thus, an urgent need exists to increase our efforts to target CIN as if it were a molecular entity. Indeed, CIN accelerates the development of anticancer drug resistance, often leading to treatment failure and disease recurrence, which limit the effectiveness of most current therapies. Identifying novel strategies to modulate CIN and to exploit the fitness cost associated with aneuploidy in cancer is, therefore, of paramount importance for the successful treatment of cancer. Modern sequencing and analytical methods greatly facilitate the identification and cataloguing of somatic copy-number alterations and offer new possibilities to better exploit the dynamic process of CIN. In this Review, we describe the principles governing CIN propagation in cancer and how CIN might influence sensitivity to immune-checkpoint inhibition, and survey the vulnerabilities associated with CIN that offer potential therapeutic opportunities.