Higher-order harmonic generation (HHG) involves ultrashort infrared pulses interacting with gas or solid targets, producing coherent radiation as short as attoseconds. Specifically, vortex laser fields with twisted wavefronts that carry orbital angular momentum have shown promise in driving HHG in gases. In our chapter work, a two-color vortex laser enables control of harmonic polarization by rotating the fundamental (800 nm), thereby manipulating vortex-harmonic light. In contrast, single-color vortex pumping drives HHG with odd-order harmonics with uniform orbital angular momentum. Generating extreme-ultraviolet vortex beams through HHG with single- and two-color vortex lasers can shape attosecond pulses with orbital angular momentum and complex patterns. These vortex harmonic beams are useful for applications such as XUV lithography, metrology, imaging, and the control of molecular chirality and dichroism.