Increase in the water scarcity and the related rise in demand of water coupled with the threating events of climate change, ultimatelywitnessed drought in the recent years to occur frequently. Therefore, Drought hydrology is drawing most of the attention. Drought which isa natural hazard can be best characterized by various hydrological and climatological parameters. In order to model drought, researchershave applied various concepts starting from simplistic model to the complex ones. The suitability of different modelling approaches andtheir negative and positive traits are very essential to comprehend. This paper is an attempt to review various methodologies utilized inmodelling of drought such as forecasting of drought, drought modelling based on probability, Global Climate Models (GCM) under climatechange scenarios. It is obtained from the present study that the past three decades have witnessed a very significant improvement in thedrought modelling studies. For the larger time window of drought forecasting, hybrid models which incorporates large scale climate indicesare promisingly suitable. Drought characterization based on copula models for multivariate drought characterization seems to have an edgeover the others. At the end some conclusive remarks are made as far as the future drought modelling and research is concerned.