摘要： Optical vortices are very attractive because they transport a well-defined orbital angular momentum (OAM) associated with the singularity of the beam. These singular beams, commonly generated in the optical regime, are used in a wide range of applications: communication, micromanipulation, microscopy, among others. The production of OAM beams in the extreme ultraviolet (XUV) and X-ray regimes is of great interest as it allows to extend the applications of optical vortices down to the nanometric scale. Several proposals have been explored in order to generate XUV vortices in synchrotrons and FEL facilities. Here, we study the generation of XUV vortices through high-order harmonic generation (HHG). HHG is a unique source of coherent radiation extending from the XUV to the soft X-ray regime, emitted in the form of attosecond pulses. When driving HHG by OAM beams, highly charged XUV vortices with unprecedented spatiotemporal properties are emitted in the form of helical attosecond beams. In this chapter, we revise our theoretical work in the generation of XUV vortices by HHG. In particular, we illustrate in detail the role of macroscopic phase matching of high-order harmonics when driven by OAM beams, which allows to control the production of attosecond beams carrying OAM.