This series of lectures consists of three parts. In the first part we will review the most commonly used methods for solving the steady and unsteady incompressible Navier-Stokes equations. Special attention will be given to the treatment of the nonlinear terms, the imposition of the incompressibility constraint and the corresponding inf-sup condition on the discrete divergence operator. Various possibilities for spatial approximation such as continuous and discontinuous finite elements, finite volumes/ finite differences, will also be reviewed. In the second part, we will review the methods for direct simulation of flow problems involving rigid particles, the so-called particulate flows. The presentation will focus on the fictitious domain method in its various forms, as well as some recent developments of schemes that allow for an easy fitting of the grid to the boundaries of the particles. Finally, the methods for direct simulation of flows involving more than one fluid will be reviewed. The emphasis of the presentation will be on the Eulerian approach, although some brief description of the Lagrangian and the Arbitrary Eulerian-Lagrangian approaches will also be given. The major difficulties with the Eulerian approach for multicomponent flows, like the tracking of the fluid-fluid interfaces, enforcing of the incompressibility, and the computation of the surface tension will be considered.