Particle-laden flows occur in many industrial and natural systems. When dealing with turbulent flow, at play in numerous situations, some stochastic approaches are combined with numerical models for the flow, leading to systems of SDEs representing near wall particles dynamics, or colliding systems of Langevin or Brownian type. In this talk we introduce and discuss numerical approximations of some typical situations. Starting with the simple case of a stochastic inertial spherical particle in turbulence (Langevin type SDE), bouncing on a wall, we discuss some new convergence results for numerical schemes. We then introduce and discuss more complex situations, such as non spherical particles or specific numerical issues dealing with agglomeration models.