Optical vortex beams carrying orbital angular momentum (OAM) have found numerous applications in optical manipulation, optical communications, quantum communication, and optical imaging in the last three decades. Meanwhile, different methods have been proposed for generating vortex beams with diverse properties. In this chapter, we review the classic methods and recent advances on optical vortex generation. After introducing the brief history and basic properties of optical vortex beams, we summarize various approaches for vortex beams generation, based on optical elements, digital devices, mode conversion, superposition of waves, and metasurfaces, etc. Moreover, we introduce the recent progress of novel vortex beams, including perfect vortex beam, fractional vortex beams, anomalous vortex beam, and vortex beams with varying OAM, and so on. The great advance in the generation of vortex beams will open up new opportunities for application of OAM.