The transport of micro- and nano- particles driven by magnetic fields has significant applications in fields such as microrobotics, flexible manufacturing, and precision medicine. In recent years, substantial progress has been made in experimental research, numerical simulations, and theoretical modeling. However, a systematic understanding of interface effects, multi-particle collective motion, motion mode regulation, and multi-field collaborative control remains lacking. This paper provides a systematic review of recent studies from the perspective of experimental fluid mechanics, focusing on the forces and dynamic behaviors of magnetic particles in low Reynolds number fluids. The review organizes three typical motion modes—translation, rotation, and near-wall rolling—corresponding to magnetic force and torque inputs. It outlines force models, velocity scaling relationships, and correction laws due to wall drag and lubrication effects under gradient and rotating fields. It also summarizes the collective dynamics of magnetic particles induced by magnetic–hydrodynamic coupling and interface geometric constraints in multi-particle systems, reflecting the non-equilibrium feedback between magnetic field input and fluid medium. The review discusses the traction transfer mechanisms between magnetic particles and droplets or vesicles in composite particle systems, presenting the interfacial dynamics of composite motion under magnetic driving. Furthermore, it summarizes the representative mechanisms and application scenarios of multi-field collaborative systems, such as magneto-acoustic, magneto-electric, and magneto-chemical systems, demonstrating the potential of cross-field driving to enhance control freedom under complex media or specific task constraints. This review aims to provide a reference for the mechanical understanding and system design of magnetic particle transport, offering foundational support for the further development of magnetically driven microsystems in biomedical fields.