Interfaces between two uids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of uid- uid interfaces is dicult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain in- sight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral inter- face extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopoten- tial approach for multi-component uids in combination with (b) an additional advection-diusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsiers.