With advancements in science and technology and market diversification needs, the development of electronic components has focused on miniaturization and high integration. At the same time, the heat generated by these electronic components increases rapidly, and the excessive accumulation of heat affects the performance and service life of the equipment; therefore, the development of high thermal conductivity materials has become an effective way to solve this problem. Over the years, polymer-based thermally conductive materials have attracted much attention because of their excellent insulating properties, chemical resistance, and easy processing performance. However, the polymers commonly used in the market are mostly highly polluting and energy-consuming petroleum-based materials whose large-scale production has seriously affected resources and the environment. As a green, low-carbon, environmentally friendly, and resource-efficient alternative material, biobased materials are expected to be a potential solution for thermal management. So far, the reported thermal conductivity of biobased high thermal conductivity composites is far from expectation. This review holistically scopes current advances in this field, focusing on the preparation process, thermal conductivity modification, and application prospects of biobased high thermal conductivity composites. Finally, we discuss the current problems and look forward to challenges and opportunities, which provide ideas for the research and development of a generation of biobased high thermal conductivity composites.