## 1 Introduction  
Mg and its alloys are hailed as green engineering materials of the 21 st century, with advantages of low density, high specific strength/stiffness, good electromagnetic shielding performance, excellent damping performance and easy recycling [1; 2; 3; 4]. However, due to their hexagonal close-packed (HCP) structure, Mg alloys exhibit relatively low absolute strength, poor plastic deformation ability at room temperature, high deformation resistance and a narrow processing window [5; 6]. Thus, how to fabricate high-strength and tough Mg alloys and study their processing routes are the key to expanding their applications, and current researchers also focus on this.  
Nowadays, researchers have recognized that plastic deformation can improve the mechanical properties of Mg alloys effectively through grain refinement, fragmentation of second phases and texture modification [7; 8; 9; 10]. Forged, extruded and rolled Mg alloys have been applied in industrial production of plates, bars and components. However, the performance potential of Mg alloys has not been effectively explored due to their relatively low strain [11; 12; 13; 14]. Severe plastic deformation (SPD) is considered the most promising process to prepare high-performance Mg alloys [15]. At present, various SPD technologieshave proven the excellent capabilities in fabricating the alloys with high strength and toughness, such as equal-channel angular pressing (ECAP), high-pressure torsion (HPT), accumulative roll bonding (ARB) and multi-directional forging (MDF). They can produce materials possessing ultrafine grains with a submicrometer or nanometer range [16; 17; 18; 19; 20]. However, most of them still remain in the research stage due to the production size, equipment and processing cost. The process research also has great potential for growth.  
MDF is currently a common process of SPD technologies used in industrial applications. It can produce ultrafine grained steels, aluminum (Al) alloys, titanium (Ti) alloys, Mg alloys, etc. [21; 22; 23; 24]. The prominent feature of this process is that the loading direction continuously changes during the deformation process, causing the material to undergo multiple deformations in different directions. MDF is typically carried out within the recrystallization temperature of (0.1-0.5) \(T_{\rm m}\), where \(T_{\rm m}\) represents the melting point. It is considered an excellent method for preparing ultrafine-grained alloys with uniformly high strength and toughness.  
For wrought Mg alloys, process parameters are an important factor affecting their microstructure, texture and mechanical properties. Deformation temperature, accumulative strain and strain rate are the main factors in MDF process to fabricate Mg alloys. It is known that reasonable process parameters can easily obtain the fine grains, dispersed secondary phases and random texture of Mg alloys, which will benefit mechanical properties [22; 23; 24]. Also, researchers [25] have found that the corrosion resistance of Mg alloys can be significantly improved by grain refinement, which can increase the grain boundary area fraction, thereby weakening the relatively high internal stress generated due to the structural mismatch between the Mg alloy oxide film and the matrix. This helps to maintain the integrity and compactness of the oxide film to better protect the matrix.  
Nowadays, Mg alloys are widely used in the development of the industrial system, and the demand for wrought Mg alloys is growing. MDF is one of the most important processes for fabricating Mg alloys with high strength and toughness. It is crucial to explore the influence mechanisms of MDF on Mg alloys. Thus, this paper will provide reference for the development of MDFed Mg alloys in the future. Specifically, recent research of Mg alloys fabricated by MDF has been reviewed in terms of their effect factors, while the deformation behavior, grain refinement, texture evolution and mechanical properties have also been discussed.