Magnetic exchange interactions and their induced magnetic structures are crucial factors in determining magnetization switching. Dzyaloshinskii-Moriya interaction (DMI) is an asymmetric exchange interaction arising from spin-orbit coupling and structural inversion symmetry breaking, which is one of the key mechanisms to induce non-collinear magnetic order and chiral magnetic structures, including magnetic Skyrmion, vortex and chiral domain wall. These magnetic structures enable novel information proceeding devices with ultralow power consumption. More importantly, non-collinear magnetic order exhibits richer and more novel physical behaviors than traditional collinear magnetic structures. With ongoing exploration and research into magnetic materials, rare-earth transition metal ferrimagnetic materials such as CoGd, CoTb, and GdFeCo have emerged as notable candidates. These materials combine the spin-orbit coupling of rare-earth elements with the magnetic exchange interactions of transition metals, leading to ultrafast magnetization dynamics, tunable magnetic structures, and rich spin transport phenomena. These properties provide an ideal material platform for studying and manipulating DMI, demonstrating significant potential in designing future high-density magnetic storage and spintronic devices. This review systematically elucidates the microscopic physical origin of DMI, outlines the fundamental characteristics of rare-earth transition metal ferrimagnetic materials, and explores the coupling mechanisms between DMI and ferrimagnetic order. We introduce the fundamental properties of RE-TM systems and their applications in spin logic devices and magnetic memory devices. We focus on discussing the physical phenomena related to DMI in RE-TM systems, including the scaling relationship of DMI in RE-TM, DMI-related spin-orbit torque effects, and the principles and applications of skyrmion-based devices, which will provide both theoretical foundations and technical guidance for the future development of advanced spintronic technologies.