Non-diffracting" beams do not spread as they propagate. This property is useful in many areas. Here, the theory, generation, properties, and applications of various "non-diffracting" beams, including the Bessel beam, Mathieu beam, and Airy beam is reviewed. Applications include imaging, micromanipulation, nonlinear optics, and optical transfection."Non-diffracting" finite energy Airy beam clearing a chamber of micro-particles.