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This thesis aims to substantially contribute to the understanding of the unsteady aerodynamics that remains unclear in the VAWTs. The analysis has been carried out by using computational fluid dynamics techniques very carefully verified with experimental data and using a modified Leishman-Beddoes dynamic stall algorithm. The results of this investigation are based on the analysis of oscillating aerofoils at constant and time-varying Reynolds and VAWTs with one, two and three blades evaluated at the tip speed ratio range of 1.5-5 using four symmetrical aerofoils and two-cambered aerofoils. The results have shown that: (i) the stall-onset angle in the VAWTs is defined by the combined effect of the tip speed ratio, pitch angle, angular frequency and relative velocity in the final value of the non-dimensional pitch rate when the angle of attack approaches the static stall angle; (ii) Under the fully attached regime, the symmetrical aerofoils performed better than the cambered aerofoils especially at the downstream zone of the rotor. This zone has shown to play the most significant role in the reduction of the overall torque coefficient and this reduction increases with the tip speed ratio, thus, a poor lift force coefficient at negative angles of attack can mitigate the advantages of a high lift/drag aerofoil observed at positive angles of attack. (iii) The curvature effect becomes more relevant with the increase of the tip speed ratio but also appears to be affected by the number of blades, therefore, a fast tool to design VAWTs needs to take into account this phenomenon in order to give reliable results. In the methods proposed in this thesis, despite being limited to the cases investigated, they demonstrate to be a potential tool to predict the unsteady loads in the VAWTs. The present investigation gives sufficient aerodynamic information to design strategies that improve VAWT performance.