Introduction -- Vortex-beam spatial-generation method -- Vortex-beam generation using the optical-fiber method -- Superposition characteristics of high-order radial Laguerre-Gaussian beams -- Transmission Characteristics of Vortex Beams -- Adaptive-optics correction technology -- Crosstalk analysis of an OAM-multiplexing system under atmospheric turbulence -- Properties of a superimposed vortex beam -- Vortex-beam detection -- Diffraction characteristics of a vortex beam passing through an optical system -- Propagation characteristics of a partially coherent vortex-beam array in atmospheric turbulence -- Propagation characteristics of scalar partially coherent vortex beams in atmospheric turbulence -- Propagation characteristics of partially coherent vector vortex beams in atmospheric turbulence -- Vortex-beam information exchange.