In this paper, we present our recent research development on single fs laser beam induced periodic structures, i.e. nanovoid array, tilted grating structures, nanograting etc, and discuss the mechanisms and promising applications of the observed periodic structures. Periodic structures can be used as grating and lens etc. Usually they are prepared by point-by-point or line by line laser scanning and using multi-beam laser interference technique. However, periodic nanovoid array was observed in transparent materials along the propagation direction of single fs laser beam. (1) By adopting a physical model which combines the nonlinear propagation of fs laser pulses with the spherical aberration (SA) effect at the interface of two mediums of different refractive indices, reasonable agreements between the simulation results and the experimental results were obtained. By comparing the fluence distributions of the case with both SA and nonlinear effects included and the case with only consideration of SA, we suggest that SA, which results from the refractive index mismatch between air and fused silica glass, is the main reason for the formation of the self-organized void array. (2) We observed self-organized microgratings in the bulk SrTiO3 crystal by scanning the laser focus in the direction perpendicular to the laser propagation axis. The groove orientations of those gratings could be controlled by changing the irradiation pulse number per unit scanning length, which could be implemented either through adjusting the scanning velocity at a fixed pulse repetition rate or through varying the pulse repetition rate at a fixed scanning velocity. (3)