This article introduces the basic concepts and related technologies of wireless communications and vortex electromagnetic waves. After that, we give a comprehensive overview of the experimental research progress of wireless communication technologies based on vortex electromagnetic waves in recent years, including microwave vortex electromagnetic wave communications, terahertz vortex electromagnetic wave communications, mid-infrared vortex electromagnetic wave communications, near-infrared vortex electromagnetic wave communications, and visible light vortex electromagnetic wave communications. At the same time, the theoretical research progress of satellite vortex laser communication technology and the experimental research progress of extended structured light (such as Bessel light beam and vector light beam) communications against obstacles and turbulence effects are introduced. At the end of the article, the challenges and prospects of vortex electromagnetic wave wireless communication technologies are also discussed. Multi-band and multi-dimensional fusion of vortex electromagnetic waves and extended structured electromagnetic waves, may provide potential solutions for multi-scenario, cross-scale, large-capacity, long-distance, and high-robustness wireless communications, and are also expected to be applied in future satellite communications.