One of the most common characteristics of cancer cells is genomic instability. Recent research has revealed that G2/M-phase checkpoint adaptation—entering mitosis with damaged DNA—contributes to genomic changes in experimental models. When cancer cells are treated with pharmacological concentrations of genotoxic agents, they undergo checkpoint adaptation; however, a small number of cells are able to survive and accumulate micronuclei. These micronuclei harbour damaged DNA, and are able to replicate and reincorporate their DNA into the main nucleus. Micronuclei are susceptible to chromothripsis, which is a phenomenon characterised by extensively rearranged chromosomes that reassemble from pulverized chromosomes in one cellular event. These processes contribute to genomic instability in cancer cells that survive a genotoxic anti-cancer treatment. This review provides insight into checkpoint adaptation and its connection to micronuclei and possibly chromothripsis. Knowledge about these mechanisms is needed to improve the poor cancer treatment outcomes that result from genomic instability.