To analyse the aerodynamic performance of wind turbine rotors, the main tool in use today is the 1D-Blade Element Momentum (BEM) technique combined with 2D airfoil data. Because of its simplicity, the BEM technique is employed by industry when designing new wind turbine blades. However, in order to obtain more detailed information of the flow structures and to determine more accurately loads and power yield of wind turbines or cluster of wind turbines, it is required to resort to more sophisticated techniques, such as Computational Fluid Dynamics (CFD). As computer resources keep on improving year by year (about ten times every five years from statistics over the last twenty years), CFD has now become a popular tool for studying the aerodynamics of wind turbines. The present thesis consists of 19 selected papers dealing with the development and use of CFD methods for studying the aerodynamics and aero-acoustics of wind turbines. The papers are written in the period from 1997 to 2008 and numbered according to the list in page v. The work consists of two parts: an aerodynamic part based on Computational Fluid Dynamics and an aero-acoustic part based on Computational Aero Acoustics for wind turbines. The main objective of the research was to develop new computational tools and techniques for analysing flows about wind turbines. A few papers deal with applications of Blade Element Momentum (BEM) theory to wind turbines. In most cases the incompressible Navier-Stokes equations in primitive variables (velocity-pressure formulation) are employed as the basic governing equations. However, since fluid mechanical problems essentially are governed by vortex dynamics, it is sometimes advantageous to use the concept of vorticity (defined as the curl of velocity). In vorticity form the Navier-Stokes equations may be formulated in different ways, using a vorticity-stream function formulation, a vorticity-velocity formulation or a vorticity-potential-stream function formulation. In  -  two different vorticity formulations were developed for 2D and 3D wind turbine flows. In  and  numerical techniques for avoiding pressure oscillations were developed when solving the velocity-pressure coupling system in the in-house EllipSys2D/3D code, which originally was developed in a cooperation between DTU (Michelsen, 1992) and Risø (Sørensen, 1995). In  –  different actuator disc techniques combined with CFD are presented. This includes actuator disc, actuator line and actuator surface techniques, which were developed to simulate flows past one or more wind turbines. In  and  a tip loss correction method that improves the conventional models was developed for use in combination with BEM or actuator/Navier-Stokes computations. A simple and efficient technique for determining the angle of attack for flow past a wind turbine rotor was developed in , and in  tunnel wall corrections for wind tunnels with closed or open test sections were developed. The second part of the thesis deals with Computational Aero-Acoustics (CAA). With the spread of wind turbines near urban areas, there is an increasing need for accurate predictions of aerodynamically generated noise. Indeed, noise has become one of the most important issues for further development of wind power, and the ability of controlling and minimising noise emission may be advantageous when competing on the world energy market. To predict generation and propagation of aerodynamic noise, it is required to solve the compressible Navier-Stokes equations. As the scales of the flow and the acoustic waves are quite different (about 1/M, M=Mach number=U/c), it is difficult to resolve them together at the same time. Hardin and Pope proposed a non-linear two-step (viscous incompressible flow and inviscid acoustic perturbation) splitting procedure for computational aero-acoustics that is suitable for both generation and propagation. The advantage of the splitting approach, as compared to the acoustic analogies, is that the source strength is obtained directly and that it accounts for sound radiation as well as scattering. In  and  an inconsistency in the original formulation of Hardin and Pope 1994 was analysed and a consistent formulation was proposed and applied to laminar flows. An aero-acoustic formulation for turbulent flows was in  developed for Large Eddy Simulation (LES), Unsteady Reynolds Averaged Navier-Stokes Simulation (URANS) and Detached Eddy Simulation (DES). In  a collocated grid / finite volume method for aero-acoustic computations was developed and implemented in the EllipSys2D/3D code. In  and  three dimensional flow-acoustic computations were carried out. Finally, the aero-acoustic formulation using high order Finite Difference schemes (Dispersion Relation Preserving (DRP) / Optimized Compact schemes) was developed in  and implemented in the EllipSys2D/3D code.