A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report, we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.