The robustness of biological performance, whether developmental or physiological, relies heavily on feedback control. The autocatalytic nature of cell proliferation makes such control especially important in tissue homeostasis, and multiple mechanisms of cell cooperation have been described—and seem to be universally necessary—just to balance cell turnover with spatially even, constant cell production, achieve physiologically desirable steady states, respond quickly to perturbations, and resist breaking down in the face of common somatic mutation. It is thus within the context of densely-connected networks of feedback control that cancers arise, yet the implications of this fact are little explored. I will discuss recent progress and current challenges in the quantitative understanding of proliferative dynamics and its control. In addition, I will argue that the fact that cancers, even as they progress, most likely retain pieces of the feedback control machinery that characterizes normal tissues, can help shed light on some of the common peculiarities of cancer, such as slow growth, arrest of benign tumors at fixed sizes, senescence or elimination of oncogene-expressing clones, dormancy, oscillatory responses to therapy, and the prevalence of hierarchical lineage structures ("cancer stem cells'').