Abstract: The application of the Immersed Boundary ~IB! method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references. @DOI: 10.1115/1.1563627# 1 CONTEXT The continuous growth of computer power strongly encourages engineers to rely on computational fluid dynamics ~CFD! for the design and testing of new technological solutions. Numerical simulations allow the analysis of complex phenomena without resorting to expensive prototypes and difficult experimental measurements. The basic procedure to perform numerical simulation of fluid flows requires a discretization step in which the continuous governing equations and the domain of interest are transformed into a discrete set of algebraic relations valid in a finite number of locations ~computational grid nodes! inside the domain. Afterwards, a numerical procedure is invoked to solve the obtained linear or nonlinear system to produce the local solution to the original equations. This process is simple and very accurate when the grid nodes are distributed uniformly ~Cartesian mesh! in the domain, but becomes computationally intensive for disordered ~unstructured! point distributions. For simple computational domains ~a box, for example! the generation of the computational grid is trivial; the simulation of a flow around a realistic configuration ~a road vehicle in a wind tunnel, for example!, on the other hand, is extremely complicated and time consuming since the shape of the domain must include the wetted surface of the geometry of interest. The first difficulty arises from the necessity to build a smooth surface mesh on the boundaries of the domain ~body conforming grid!. Usually industrially relevant geometries are defined in a CAD environment and must be translated and cleaned ~small details are usually eliminated, overlapping surface patches are trimmed, etc! before a surface grid can be generated. This mesh serves as a starting point to generate the volume grid in the computational domain. In addition, in many industrial applications, geometrical complexity is combined with moving boundaries and high Reynolds numbers. This requires regeneration or deformation of the grid during the simulation and turbulence modeling, leading to a considerable increase of the computational difficulties. As a result, engineering flow simulations have large computational overhead and low accuracy owing to a large number of operations per node and high storage requirements in combination with low order dissipative spatial discretization. Given the finite memory and speed of computers, these simulations are very expensive and time consuming with computational meshes that are generally limited to around one million nodes. In view of these difficulties, it is clear that an alternative numerical procedure that can handle the geometric complexity, but at the same time retains the accuracy and high efficiency of the simulations performed on regular grids, would represent a significant advance in the application of CFD to industrial flows.