For decades, it has always been a dream of mankind to create self-bending of light in free space and even a boomerang of light as often seen in science fiction. Recently, Airy beams, along with their generalized self-accelerating beams, have attracted a great deal of attention due to their novel properties such as non-diffraction, self-bending, and self-healing. These unconventional optical beams not only have been realized in experiment, but also have wide application prospects, such as for particle manipulation, plasma channels, surface plasmons, electron acceleration, super-resolution imaging, transmission in turbulent environment, and guiding electric discharge. These application prospects make self-accelerating beams an attracting and exciting frontier of research. Here, we present an overview of the development and recent advances about self-accelerating beams mediated by phase modulation, including the generation and propagation properties of self-accelerating beams, and their extension and control in both spatial and temporal domains, with a focus on discussion of their novel applications in several areas.