International audienceIn drilling operations, the drillstring interaction with the borehole gives rise to a wide variety of undesired oscillations. The main types of drilling vibrations are torsional (stick-slip), axial (bit-bounce) and lateral (whirling). The analysis and modeling of rotary drilling vibrations is a topic whose economical interest has been renewed by recent oilfields discoveries leading to a growing literature. This paper summarizes the most popular modeling strategies allowing the oscillatory behavior analysis of the physical system