Clinical research generally focuses on results involving a statistical mean with little attention in trial design to patients who respond considerably better or worse than average. Exploring the reasons underlying an "atypical response" will increase understanding of the mechanisms involved in cancer progression and treatment resistance, accelerate biomarker identification, and improve precision medicine by allowing clinicians to prospectively select optimal treatments. Based on our review, we suggest two ways to move this field forward. First, we suggest that clear categorization of "atypical responders" is needed. This encompasses three sub-categories of patients: "exceptional responders" (those with an unusually favorable treatment response), "rapid progressors" (patients demonstrating an unusually poor or no therapeutic response), and "exceptional survivors" (patients who have far outlived their initial prognosis). Such categorization may depend upon the clinical context and disease subtype. Second, we suggest that atypical responses may be due not only to somatic mutations in tumors, but also to inherited polymorphisms in non-tumor tissue, host and tumor environments, lifestyle factors, co-morbidities, use of complementary and integrative medicine, and the interaction among these components. Here, we summarize new research initiatives exploring atypical responses, the potential reasons for atypical responses, and a strategic call to action. Rigorous studies of normal and atypical responses to treatment will be needed to strengthen understanding of the role of non-tumor factors. Clinical trial design for targeted and other types of therapies should be enhanced to collect data in a standardized manner beyond tumor genetics, resulting in more thorough study of the whole patient.