Optical vortex carries optical orbital angular momentum because its Poynting vector is featured by a spiral phase rotating around its propagation axis, and thus its generation and transformation are always accompanied by the change of orbital angular momentum. Orbital angular momentum has attracted intensive attention in the fields of classical optics and quantum information. At present, a series of mature methods of orbital angular momentum generationand modulation have been developed, of which photoaligned liquid crystal fork grating is one important type. Photoalignment is suitable for high-resolution and free fabrication of liquid crystal microstructures, greatly enhancing the capability of generating and modulating of optical vortices and their arrays. This paper summarizes researches on generations and modulations of optical vortices with photoaligned liquid crystal fork gratings, mainly focuses on the recent progress of binary and polarization fork gratings, Damman encoded fork gratings and spiral structured Damman fork gratings in the generations of optical vortices and their arrays, as well as broadband applications.