The identification of specific genetic alterations that drive the initiation and progression of cancer and the development of targeted drugs that act against these driver alterations has revolutionized the treatment of many human cancers. While substantial progress has been achieved with the use of such targeted cancer therapies, resistance remains a major challenge that limits the overall clinical impact. Hence, despite progress, new strategies are needed to enhance response and eliminate resistance to targeted cancer therapies in order to achieve durable or curative responses in patients. To date, efforts to characterize mechanisms of resistance have primarily focused on molecular events that mediate primary or secondary resistance in patients. Less is known about the initial molecular response and adaptation that may occur in tumor cells early upon exposure to a targeted agent. Although understudied, emerging evidence indicates that the early adaptive changes by which tumor cells respond to the stress of a targeted therapy may be crucial for tumor cell survival during treatment and the development of resistance. Here, we review recent data illuminating the molecular architecture underlying adaptive stress signaling in tumor cells. We highlight how leveraging this knowledge could catalyze novel strategies to minimize or eliminate targeted therapy resistance, thereby unleashing the full potential of targeted therapies to transform many cancers from lethal to chronic or curable conditions.