Modern techniques to model torsional drill string vibration have positive impact to the efficiency of oil and gas drilling. The need for torsional model is evident from their detrimental effect to the bottom hole assembly (BHA) fitness. The model can cater planning for more efficient parameter selections for BHA and controlling surface parameter to reduce such vibration. In this paper, the models for torsional vibrations are classified based on their functional concept. The validation techniques are also reported with each classification of the model for torsional vibrations. © 2006-2016 Asian Research Publishing Network (ARPN).