Bioeconomy and circular economy approaches are being adopted by an increasing number of international organizations, governments and companies to enhance sustainability. Concerns have been raised about the implications for biodiversity. Here, we present a review of current research on the two approaches to determine their relationship to each other and to other economic models, their impact on sustainability and their relationship with biodiversity. Bioeconomy and circular economy are both poorly defined, inconsistently implemented and inadequately measured, and neither provides a clear pathway to sustainability. Many actors promote goals around economic growth above environmental issues. Biodiversity is often addressed indirectly or inadequately. Furthermore, many traditionally disadvantaged groups, including women and indigenous people, may be neglected and rarely engage or benefit. These challenges are compounded by capacity gaps and legal and governance complexities around implementation, influenced by traditional mindsets and approaches. Countries and companies need to plan their sustainability strategies more explicitly around the biodiversity they impact. Opportunities include the relevance and timeliness of sustainable economics for delivering Sustainable Development Goals in a post-COVID world, the existence of work to be built on, and the diversity of stakeholders already engaged. We propose five main steps to ensure the sustainability of economic approaches. Ultimately, we can ensure sustainability only by starting to shift mindsets and establishing a more focused agenda for bioeconomy and circular economy that puts species, ecosystems and the wellbeing of local people at the center.