With the rapid development of artificial intelligence (AI) agents and large model applications, the demand for computing power is becoming increasingly dynamic, platform-based, and globally distributed. The generation and invocation of computing tasks are gradually shifting from manual triggering and local execution to autonomous generation by AI agents, cross-platform invocation, and cross-border execution. This transition is profoundly reshaping the conventional security boundary of power‒computing coordination, which has traditionally been centered on local power grids and data centers. The coupling among data flows, computing flows, and energy flows is consequently becoming more complex, and the security of power‒computing interaction is evolving from single-system protection toward comprehensive risk governance under cross-domain coupling. Focusing on the emerging security issues associated with cross-border power‒computing interaction driven by AI agents, this study reviews the development patterns, operational characteristics, security risks, protection technologies, and future research directions of cross-border power‒computing interaction. Moreover, the evolutionary characteristics of cross-border power‒computing interaction are analyzed in terms of system boundaries, scheduling mechanisms, and load characteristics, and the coupling relationships among computing demand generation, cross-domain interaction, and power‒load response are clarified. Key security risks related to data security, computing power scheduling security, power‒load manipulation, and cross-domain cascading failures are summarized, revealing a risk evolution chain comprising degraded data trustworthiness, distorted scheduling decisions, abnormal load reconfiguration, and cross-domain cascading propagation. Additionally, protection technologies involving data protection, scheduling governance, load control, and system monitoring are summarized, and their applicability and limitations in cross-border interaction environments are discussed. Future research directions are further outlined in the areas of computing demand generation, computing scheduling constraints, cross-domain collaborative defense, and endogenous security architectures. This study is expected to provide theoretical support and practical guidance for developing secure and trustworthy cross-border power‒computing interaction systems.