Targeted therapies directed against oncogenic signaling addictions, such as ALK inhibitors (ALKi) in ALK+ NSCLC, tend to induce strong and durable clinical responses. However, targeted therapies are not curable, as subsets of tumor cells survive, persisting under therapy. Subsequently, these residual populations evolve resistance, manifested as cancer relapse. Massive research and development efforts have been directed to overcoming resistance and achieving cures. However, despite identifying large numbers of molecular drivers of resistance and extending remission times, targeted therapies remain non-curable, and resistance remains inevitable. The relatively slow pace of therapeutic progress reflects multiple challenges, including both well-appreciated and emerging ones. Correct identification of the challenges is essential for directing research efforts necessary for moving from incremental progress to major breakthroughs. In addition to the obvious challenges of inter-tumor heterogeneity, identification of specific resistance mechanisms and drug availability, the once emergent challenge of intra-tumor heterogeneity is generally well appreciated. Less recognized is the fundamental challenge of evolvability of neoplastic populations, i.e., the ongoing ability to generate heritable phenotypic variability that can fuel the evolution of resistance. Even less appreciated is the emergent multifactorial nature of therapy persistence and resistance, i.e., that, even at the level of individual tumor cells, persistence and resistance are not necessarily reducible to a single mechanistic driver. Instead, the evolution of resistance develops as trajectories in adaptive and epigenetic landscapes, shaped by an integrated input of multiple tumor cell intrinsic, microenvironmental, and systemic factors. Addressing the fundamental issue of therapy resistance requires the acknowledgment of the complex spatiotemporal dynamics of evolving resistance and the development of therapeutic strategies that consider integrative inputs that shape loss of therapy sensitivity while hindering the ability of tumors to adapt.