The common intuition of light propagating along a straight path was challenged by the discovery of the Airy beam. Optical beams with an Airy profile undergo self-bending and propagate along parabolic trajectories. Airy wavepackets, on the other hand, can self-accelerate during propagation. Due to their unusual and unique properties, Airy beams and pulses have been used in several applications such as microparticle manipulation, micromachining, and curved plasma channel generation. The future prospects of such beams are vast and they can be extended to other areas including plasmonics, microwaves and acoustics.