Human cancers comprise an heterogeneous array of diseases with different progression patterns and responses to therapy. However, they all develop within a host context that constraints their natural history. As it occurs with the diversity of organisms, one can conjecture that there is order in the cancer multiverse. Is there a way to capture the broad range of tumor types within a space of the possible? Here we define the oncospace, a coordinate system that integrates the ecological, evolutionary and developmental components of cancer complexity. The spatial position of a tumor results from its departure from the healthy tissue along these three axes, and progression trajectories inform about the components driving malignancy across cancer subtypes. We postulate that the oncospace topology encodes new information regarding tumorigenic pathways, subtype prognosis and therapeutic opportunities: treatment design could benefit from considering how to nudge tumors towards empty evolutionary deserts in the oncospace.