Orbital angular momentum (OAM) has aroused a widespread interest in many fields, especially in telecommunications due to its potential for unleashing new capacity in the severely congested spectrum of commercial communication systems. Beams carrying OAM have a helical phase front and a field strength with a singularity along the axial center, which can be used for information transmission, imaging and particle manipulation. The number of orthogonal OAM modes in a single beam is theoretically infinite and each mode is an element of a complete orthogonal basis that can be employed for multiplexing different signals, thus greatly improving the spectrum efficiency. In this paper, we comprehensively summarize and compare the methods for generation and detection of optical OAM, radio OAM and acoustic OAM. Then, we represent the applications and technical challenges of OAM in communications, including free-space optical communications, optical fiber communications, radio communications and acoustic communications. To complete our survey, we also discuss the state of art of particle manipulation and target imaging with OAM beams.