The burgeoning fields of robot learning and embodied AI have triggered an increasing demand for large quantities of data. However, collecting sufficient unbiased data from the target domain remains a challenge due to costly data collection processes and stringent safety requirements. Consequently, researchers often resort to data from easily accessible source domains, such as simulation and laboratory environments, for cost-effective data acquisition and rapid model iteration. Nevertheless, the environments and embodiments of these source domains can be quite different from their target domain counterparts, underscoring the need for effective cross-domain policy transfer approaches. In this paper, we conduct a systematic review of existing cross-domain policy transfer methods. Through a nuanced categorization of domain gaps, we encapsulate the overarching insights and design considerations of each problem setting. We also provide a high-level discussion about the key methodologies used in cross-domain policy transfer problems. Lastly, we summarize the open challenges that lie beyond the capabilities of current paradigms and discuss potential future directions in this field.