In surfaces irradiated by short laser pulses, Laser Induced Periodic Surface Structures (LIPSS) have been observed on all kind of materials for over forty years. These LIPSS, also referred to as ripples, consist of wavy surfaces with periodicity equal or smaller than the wavelength of the laser radiation. Unfortunately, the physical phenomena explaining ripple initiation, growth and transitions toward other patterns are still not fully understood. Models, explaining ripple initiation and growth, based on the laser parameters, such as the wavelength and the angle of incidence, are frequently discussed in literature. This paper presents the most promising models, their ability and limitations to predict experimental results.