## 1 Introduction  
From [PERSON]'s theory, it is well known that electromagnetic (EM) waves carry both linear momentum and angular momentum. The angular momentum is composed of two parts: spin angular momentum (SAM) corresponding to the polarization of the EM wave and orbital angular momentum (OAM) associated to the spatial distribution of the EM wave.  
SAM of an EM wave has been recognized for a long time and it carries \(\pm\hbar\) per photon. However, OAM has only attracted valuable attention since 1992 when [PERSON] et al. [1] showed that Laguerre-Gaussian (LG) beams possess an orbital angular momentum of \(\hbar\) per photon, where \(l\) is an integer and refers to the topological charge (order) of the OAM mode, i.e., the number of phase twists around the vortex. In 1994, [PERSON] et al. further discussed the relationship between non-paraxial beams and angular momentum since LG beams are not exact solutions of the full [PERSON]'s theory that are only the solutions of the paraxial wave equation [2]. Under the condition of non-paraxial approximation, theoretical calculation results show that OAM still depends on the topological charge \(l\). As long as the beams contain spiral phase, they will carry an OAM mode. It provides a simpler way to generate OAM, that is, vortex beams can be excited with a plane wave. While the phase of a plane wave is constant on the wavefront, the phase \(\alpha\) of an OAM wave undergoes a linear variation along the angular coordinate with \(\alpha=l\varphi\). The field hence varies as \(\mathrm{e}^{-\beta l\varphi}.f_{l}(r)\mathrm{e}^{-\beta lz}\), where \(k\) is the wave vector, \(z\) is the propagation axis and \(f_{l}(r)\) represents the field variation along the radial coordinate.  
Early studies in optical regime concerning the interaction of OAM with matter raised applications in optical tweezers [3; 4], optical drive of micro-machines [5], atoms trapping and guiding [6; 7], microscopy [8], and photon entanglement [9]. In the radiofrequency (RF) domain, OAM has been firstly proposed to improve spectral efficiency in radio communications by creating multiple propagation sub-channels corresponding to the twisting degree of the EM wave [10; 11; 12; 13; 14]. Other possible applications of OAM include object identification [15] and radars [16; 17; 18; 19; 20].  
It is common to generate OAM beams in the optical domain, especially when the programmable spatial light modulator (SLM) is available [21]. Existing optical devices can also provide mature schemes to manipulate OAM beams such as combination, splitting, collimation, concentration, and detection [22; 23; 24; 25]. However, in RF and microwave domains, the wavelength is much longer than in optics, and therefore it is difficult to manipulate microwave OAM beams, such as beam combining and splitting, since coaxial transmission cannot be easily ensured. Therefore, for applications in microwave domain, the OAM wave generation method is very important to ensure optimal performances of the whole system. The main goals of this review work is to present an overview of the OAM beam generation through the use of metasurfaces. The paper is structured as follows: Section 1 presents a brief introduction on OAM and Section 2 focuses on Laguerre-Gaussian (LG) beams carrying OAM. In Section 3, we present the mostly used classical methods to generate vortex waves and Section 4 deals with the use of metasurfaces for OAM beam generation. Finally, Section 5 serves as a general conclusion.