Fluid transport modeling in three-dimensional boundaries of toroidal confinement devices is reviewed with the emphasis on a Monte-Carlo approach to simulate detached plasmas. The loss of axisymmetry in such configurations presents a major challenge for numerical implementation of the standard fluid model widely applied to fusion experimental devices. A large-scale effort has been made to address this problem under complementary aspects including different magnetic topologies and numerical techniques. In this paper, we give a brief review of the different strategies pioneered and the challenges involved. A more detailed description is provided for the Monte-Carlo code—EMC3-Eirene, where the physics model and the basic idea behind the applied Monte-Carlo method are presented. The focus is put on its applications to detachment studies for stellarators and tokamaks. Here, major achievements and difficulties encountered are described. Model limitations and further development plans are discussed.