The Dzyaloshinskii-Moriya interaction (DMI), as an antisymmetric exchange interaction, is one of the key mechanisms for stabilizing noncollinear chiral magnetic structures. It plays an important role in the multi-field control of magnetic dynamics and provides a new pathway for designing and developing high-density, low-power, non-volatile spintronic devices. This study focuses on the manipulation of magnetic dynamics driven by DMI, reviewing theoretical studies and frontier technological explorations on DMI-assisted current-driven magnetic dynamics and DMI-based electric field control of magnetic dynamics. Since Dzyaloshinskii first proposed this kind of antisymmetric exchange interaction in 1957, the research on DMI has developed from fundamental physical research to practical device application exploration. The DMI theoretical framework has been progressively refined through the developments by Moriya, Fert, and Levy. Moreover, DMI materials have also expanded from B20-type compounds to heterostructures and two-dimensional materials. The study of DMI-driven magnetic dynamics has opened a new way for the next-generation spintronic devices. DMI-assisted current-driven magnetic dynamics include deterministic magnetization switching under zero magnetic field through the synergistic effect of DMI and spin-orbit torques, as well as low-power current-driven dynamics achieved through effective coupling between spin current and chiral magnetic texture. Electric control of magnetic dynamics based on DMI includes various physical mechanisms for electric field control of DMI, electric field manipulation strategies for DMI-dominated topological magnetic states, and all-electric DMI torque-driven magnetic dynamics that transfer spin angular momentum through topological magnetic structures. In recent advances, the critical current density for field-free magnetization switching has been reduced to 10⁵ A/cm², and skyrmion velocities have reached the km/s range. A variety of methods for electric-field control of DMI, mechanisms for manipulating topological magnetic structures through electric fields, and all-electric device design schemes are proposed. These advances reflect significant progress of DMI-driven magnetic dynamics. However, there are still substantial challenges in the fields of magnetic dynamics theory, DMI material development, and device applications. Addressing these challenges will continue to promote breakthroughs in DMI-related theoretical innovations, material design, and device applications, contributing to the development of the next-generation low-power, high-performance spintronic devices.