<p>The nonlinear characteristics of flexible-joint robotic manipulators (FJRMs)—namely “joint flexibility–coupling–vibration”—have become a primary bottleneck that limits the realization of high-precision operation and safe human–robot collaboration in industrial, aerospace, service, and medical applications. To systematically summarize the main threads and frontier advances in dynamics modeling in this field, this paper analyzes 1180 related publications indexed in the Web of Science database from 2000 to 2025 and employs bibliometric methods to critically interpret the developmental trajectory and global research landscape. On this basis, key modeling approaches for FJRMs are reviewed from two complementary perspectives: physics-based mechanisms and artificial intelligence, with an in-depth assessment across multiple dimensions. For physics-based modeling, we examine modeling methods for flexible-joint structural representations and major nonlinear factors—such as friction, backlash, and transmission error—and summarize strategies for coupled modeling under joint-and-link dual flexibility. For AI-based modeling, we trace the evolution from classical neural networks to physics-prior-driven paradigms and clarify both the strengths and challenges of data-driven approaches in fitting complex dynamics. By comparing the principal characteristics, advantages, and limitations of these two categories, we argue that physics–data fusion modeling is a critical direction for balancing accuracy and efficiency in future developments. Finally, we discuss emerging trends in unified modeling frameworks, online evolutionary capability, and system-level intelligence, thereby providing theoretical references for high-performance control and engineering applications of FJRMs.</p>