The prospective identification and therapeutic targeting of oncogenic tyrosine kinases with tyrosine kinase inhibitors (TKIs) has revolutionized the treatment for patients with non-small cell lung cancer (NSCLC). TKI therapy frequently induces dramatic clinical responses in molecularly defined cohorts of patients with lung cancer, paving the way for the implementation of precision medicine. Unfortunately, acquired resistance, defined as tumor progression after initial response, seems to be an inevitable consequence of this treatment approach. This brief review will provide an overview of the complex and heterogeneous problem of acquired resistance to TKI therapy in NSCLC, with a focus on EGFR-mutant and ALK-rearranged NSCLC. In vitro models of TKI resistance and analysis of tumor biopsy samples at the time of disease progression have generated breakthroughs in our understanding of the spectrum of mechanisms by which a tumor can thwart TKI therapy and have provided an important rationale for the development of novel approaches to delay or overcome resistance. Numerous ongoing clinical trials implement strategies, including novel, more potent TKIs and rational combinations of targeted therapies, some of which have already proven effective in surmounting therapeutic resistance.