Bioeconomy is proposed as a solution to reduce reliance on fossil resources. However, bioeconomy is not always inherently circular and can mimic the conventional take, make, consume, dispose linear economic model. Agricultural systems will be relied on to provide food, materials, and energy, so unless action is taken, demand for land will inevitably exceed supply. Bioeconomy will have to embrace circularity to enable production of renewable feedstocks in terms of both biomass yield and maintaining essential natural capital. The concept of biocircularity is proposed as an integrated systems approach to the sustainable production of renewable biological materials focusing on extended use, maximum reuse, recycling, and design for degradation from polymers to monomers, while avoiding the "failure" of end of life and minimizing energy demand and waste. Challenges are discussed including sustainable production and consumption; quantifying externalities; decoupling economic growth from depletion; valuing natural ecosystems; design across scales; renewable energy provision; barriers to adoption; and integration with food systems. Biocircularity offers a theoretical basis and measures of success, for implementing sustainable circular bioeconomy.