Sustainable energy development consists of design, planning, and control optimization problems that are typically complex and computationally challenging for traditional optimization approaches. However, with developments in artificial intelligence, bio-inspired algorithms mimicking the concepts of biological evolution in nature and collective behaviors in societies of agents have recently become popular and shown potential success for these issues. Therefore, we investigate the latest research on bio-inspired approaches for smart energy management systems in smart homes, smart buildings, and smart grids in this paper. In particular, we give an overview of the well-known and emerging bio-inspired algorithms, including evolutionary-based and swarm-based optimization methods. Then, state-of-the-art studies using bio-inspired techniques for smart energy management systems are presented. Lastly, open challenges and future directions are also addressed to improve research in this field.