Background: For decades, scientists have attempted to provide a sustainable development framework that integrates goals of environmental protection and human development. The Planetary Boundaries concept (PBc)-a framework to guide sustainable development-juxtaposes a 'safe operating space for humanity' and 'planetary boundaries', to achieve a goal that decades of research have yet to meet. We here investigate if PBc is sufficiently different to previous sustainability concepts to have the intended impact, and map how future sustainability concept developments might make a difference. Design: We build a genealogy of the research that is cited in and informs PBc. We analyze this genealogy with the support of two seminal and a new consumer-resource models, that provide simple and analytically tractable analogies to human-environment relationships. These models bring together environmental limits, minimum requirements for populations and relationships between resource-limited and waste-limited environments. Results: PBc is based on coherent knowledge about sustainability that has been in place in scientific and policy contexts since the 1980s. PBc represents the ultimate framing of limits to the use of the environment, as limits not to single resources, but to Holocene-like Earth system dynamics. Though seldom emphasized, the crux of the limits to sustainable environmental dynamics lies in waste (mis-)management, which sets where boundary values might be. Minimum requirements for populations are under-defined: it is the distribution of resources, opportunities and waste that shape what is a safe space and for whom. Discussion: We suggest that PBc is not different or innovative enough to break 'Cassandra's dilemma' and ensure scientific research effectively guides humanity towards sustainable development. For this, key issues of equality must be addressed, un-sustainability must be framed as a problem of today, rather than projected into the future, and scientific foundations of frameworks such as PBc must be broadened and diversified.