The hydrodynamic performance of the common three-blades horizontal axis current turbine (HAMCT) is computationally investigated to seek paths of improvement. Two computational approaches are used, namely the Blade Element Method (BEM) and Computational Fluid Dynamics (CFD)-Reynolds Averaged Navier Stokes (RANS). Two BEM codes were written for steady and unsteady calculations. Both account for hub/tip losses, turbulent wake effect and stall delay. Dynamic wake model was used for the unsteady BEM. Ansys is used for CFD-RANS. Three cases are studied; (i) Hydrodynamic improvement by replacing the common low Reynolds number asymmetric E387 profile with its CIRCLE previously-redesigned A7 profile calling for continuous surface curvature. This yields better high-angle of attack (AOA) performance. As result the A7 turbine outperforms the E387 turbine for low tip speed ratio (TSR) from mild improvement for the optimally twisted blade to a much higher improvement for the non-twisted blade. (ii) The dual-rotor turbine, where each rotor is optimally pitch-fixed for its upstream velocity, thus fitting rectilinear tidal current with no need of pitch control. Symmetric profiles outperform the asymmetric profiles when the rear rotor is correctly used, yielding an increase of up to 20% in the combined power according to the BEM coupled with the Park wake model. An analytical estimate backs this estimate. RANS is used to assess and improve the Park model. (iii) Surface wave effect is investigated for HAMCT close to the surface using BEM coupled with gravity wave theory and CFD. For the first time, effect of large waves is investigated to show the turbine's non-linear time response at low TSR. Blade loading, power spectra and time averaged proprieties are also analysed. All computations were compared to experimental results when available, generally yielding good agreement. Cases of disagreement are also discussed.