Abstract <p>To date, many different types and modifications of axicons (refractive, diffractive, micro- and meta-axicons) have been proposed, providing a wide range of functionality from generating laser beams extended along the optical axis to forming vortex and annular beams. This diversity of axicons arose with the development of existing and new approaches to calculating optical elements in response to the expansion of their application areas in optical manipulation, tight focusing, polarization transforming, materials processing, plasma channel formation, optical imaging, optical microscopy, and others. This review is devoted to a brief discussion of the various types of modern axicons and their applications.</p>