  Interfaces between two fluids are ubiquitous and of special importance for
industrial applications, e.g., stabilisation of emulsions. The dynamics of
fluid-fluid interfaces is difficult 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 insight into the physics of interfaces. In the
present article, we restrict ourselves to systems with dimensions comparable to
the lateral interface 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 pseudopotential approach for
multi-component fluids in combination with (b) an additional
advection-diffusion component for surfactant modelling and (c) a molecular
dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.
