Laser-induced periodic surface structures (LIPSSs) consist of regular wavy surface structures, or ripples, with amplitudes and periodicity in the sub-micrometer range. A summary of experimentally observed LIPSSs is presented, as well as our model explaining their possible origin. Linearly polarized continuous wave (cw) or pulsed laser light, at normal incidence, can produce LIPSSs with a periodicity close to the laser wavelength, and direction orthogonal to the polarization on the surface of the material. Ripples with a periodicity (much) smaller than the laser wavelength develop when applying laser pulses with ultra-short durations in the femtosecond and picosecond regime. The direction of these ripples is either parallel or orthogonal to the polarization direction. Finally, when applying numerous pulses, structures with periodicity larger than the laser wavelength can form, which are referred to as “grooves”. The physical origin of LIPSSs is still under debate. The strong correlation of the ripple periodicity to the laser wavelength, suggests that their formation can be explained by an electromagnetic approach. Recent results from a numerical electromagnetic model, predicting the spatially modulated absorbed laser energy, are discussed. This model can explain the origin of several characteristics of LIPSSs. Finally, applications of LIPSSs will be discussed.