The need for energy and electricity has been increasing globally, and this means more power is required from the power plants. Power plants, however, will then continue harming the earth because of the greenhouse gasses produced while generating energies that contribute to global warming. Using renewable sources to produce clean energies is one of the sustainable methods to deal with such challenges. Wind energy is one of the renewable sources, which is accessible anywhere on earth, creating green energy. Wind turbines are mainly categorized into Horizontal Axis Wind Turbines (HAWT) and Vertical Axis Wind Turbines (VAWT). This paper firstly presents a general comparison between the HAWTs and VAWTs. Then, it presents mathematical modelling for the aerodynamic factors of HAWT and Darrieus VAWT to assist the researchers to understand some key design aspects of wind turbines, such as lift/drag ratio, tip speed ratio, power coefficient, and torque coefficient. Also, this paper presents a review of the aerodynamic performance of the recent VAWT designs to help researchers to identify and choose the best model among the Savonius and Darrieus rotors for further development or designing a new model at different wind conditions. This comparison review shows that for a large scale HAWT upwind 3 bladed wind turbines are the most optimum. The helical Savonius rotors perform better by having positive torque coefficient at all azimuth angles. Moreover, helical Darrieus was found to produce lesser noise and suitable for conventional areas. hybrid Savonius-Darrieus rotors can solve the self-starting challenge of the VAWTs, and they are suitable at low wind speeds. At last, this review shows some of the recent hybrid Savonius-Darrieus rotors which would help to solve the low efficiency of Savonius rotor and self-starting challenge of Darrieus rotors.