Integrated sensing and communications (ISAC) technology, known for its efficient utilization of frequency bands and hardware, has emerged as a key solution to optimize spectrum resources and reduce hardware costs. Nowadays, designing an energy-efficient ISAC system to advance the green technology is crucial, particularly in the radio frequency (RF) chain which can offer significant energy-saving opportunities. Consequently, the existing RF chain design of the ISAC system is reviewed. To achieve the green communication goals, an in-depth look at ISAC design with several RF chain structures and related energy-saving methods is presented. Initially, an overview of the current ISAC RF chain designs in transmitters or receivers is presented, focusing on energy-efficient solutions and optimizing the system performance. Subsequently, several system structures equipped with innovative RF chains are introduced, aimed at reducing the system power consumption, along with the corresponding signal processing methods. Finally, future directions of the ISAC research and potential challenges are discussed.