Targeting mutant proteins and associated signaling pathways of driver oncogenes by small molecule kinase inhibitors (KIs) are a promising strategy of cancer therapy. However, despite the initial success of treatment, KIs often become ineffective as intrinsic and acquired resistance. This article reviews the English-language literature to explore the underlying mechanisms of drug resistance and to present a challenge for developing drugs to overcome resistance. Mechanisms of acquired resistance include 1) the selection of pre-existing subclones with other mutations, 2) the emergence of secondary mutations in the target kinase domain, 3) upregulation of kinases both within the same kinase family and their related kinase families, as well as activation of alternative bypass pathways, 4) epithelial-mesenchymal transition, 5) overexpression of pro-survival Bcl-2 family proteins and 6) drug efflux mechanisms. Currently available methods are to obtain tumor biopsy samples at recurrence or progression if the tumor lesion is accessible to a biopsy and to use the second-and third-generation KIs based on the individual need of each patient. Furthermore, recent computational challenges provide design principles to prevent the development of drug resistance. In conclusion, we provide an overview of the postulated resistance mechanisms and highlight the future direction of computational structure-based design of new potent KIs.