Cancer drug resistance continues to be a major impediment in medical oncology. Clinically, resistance can arise prior to or as a result of cancer therapy. In this review, we discuss different mechanisms adapted by cancerous cells to resist treatment, including alteration in drug transport and metabolism, mutation and amplification of drug targets, as well as genetic rewiring which can lead to impaired apoptosis. Tumor heterogeneity may also contribute to resistance, where small subpopulations of cells may acquire or stochastically already possess some of the features enabling them to emerge under selective drug pressure. Making the problem even more challenging, some of these resistance pathways lead to multidrug resistance, generating an even more difficult clinical problem to overcome. We provide examples of these mechanisms and some insights into how understanding these processes can influence the next generation of cancer therapies.