This article explores the challenges of continuum and magnetic soft robotics for medical applications, extending from model development to an interdisciplinary perspective. First, we established a unified model framework based on algebra and geometry. The research progress and challenges in principle models, data-driven, and hybrid modeling were then analyzed in depth. Simultaneously, a numerical analysis framework for the principle model was constructed. Furthermore, we expanded the model framework to encompass interdisciplinary research and conducted a comprehensive analysis, including an in-depth case study. Current challenges and the need to address meta-problems were identified through discussion. Overall, this review provides a novel perspective on understanding the challenges and complexities of continuum and magnetic soft robotics in medical applications, paving the way for interdisciplinary researchers to assimilate knowledge in this domain rapidly.