We demonstrate the first light sheet microscope using propagation invariant, accelerating Airy beams that operates both in single- and two-photon modes. The use of the Airy beam permits us to develop an ultra compact, high resolution light sheet system without beam scanning. In two-photon mode, an increase in the field of view over the use of a standard Gaussian beam by a factor of six is demonstrated. This implementation for light sheet microscopy opens up new possibilities across a wide range of biomedical applications, especially for the study of neuronal processes.