The Internet of Things (IoT) employs sensors and the Internet for information exchange, enabling intelligent identification, monitoring, and management, which has deeply impacted various sectors such as power, medical care, and security, transforming social activities and lifestyles. Regrettably, IoT systems suffer from two main challenges, namely sustainability and security. Hence, pondering how to enhance sustainable and energy-efficient practices for IoT systems to mitigate risks becomes a worthwhile endeavor. To address this issue, we conduct a survey of energy-aware security mechanisms in the Internet of Things. Specifically, we examine the challenges that IoT is facing in terms of energy efficiency and security, and we inspect current energy-saving and privacy-preserving technologies for IoT systems. Moreover, we delineate a vision for the future of IoT, emphasizing energy-aware security mechanisms. Finally, we outline the challenges encountered in achieving energy-aware security mechanisms, as well as the direction of future research. Motivated by this study, we envision advancements in the IoT that not only harness the benefits of science and technology but also enhance the security and safety of our data.