This chapter is devoted to the treatment of complex geometries. The choices of grid type, grid generation approaches in complex geometries, grid properties, velocity components and variable arrangements are discussed. FD and FV methods are revisited, and the features special to complex geometries (like non-orthogonal, block-structured and unstructured grids, non-conformal grid interfaces, control volumes of arbitrary shape, overlapping grids, etc.) are described. Special attention is paid to the pressure-correction equation and boundary conditions. Some illustrative examples of steady and unsteady, two- and three-dimensional laminar flows computed using provided codes based on the fractional-step and SIMPLE algorithms are presented and discussed; evaluation of discretization errors and comparison of results obtained using different grid types (trimmed Cartesian and arbitrary polyhedral) and commercial CFD-software are also included.