  With the rapid development of studies involving droplet microfluidics, drug
delivery, cell detection, and microparticle synthesis, among others, many
scientists have invested significant efforts to model the flow of these
fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics
and the interactions of fluid-filled bodies, several methods have been
developed. The objective of this review is to present a compact foundation of
the methods used in the literature in the context of lattice Boltzmann methods.
For hydrodynamics, we focus on the lattice-Boltzmann method due to its specific
ability to treat time and spatial-dependent boundary conditions and to
incorporate new physical models in a computationally efficient way. We split
the existing methods into two groups with regard to the interfacial boundary:
fluid-structure and fluid-fluid methods. The fluid-structure methods are
characterised by the coupling between fluid dynamics and mechanics of the
flowing body, often used in applications involving membranes and similar
flexible solid boundaries. We further divide fluid-structure-based methods into
two subcategories, those which treat the fluid-structure boundary as a
continuum medium and those that treat it as a discrete collection of individual
springs and particles. Next, we discuss the fluid-fluid methods, particularly
useful for the simulations of fluid-fluid interfaces. We focus on models for
immiscible droplets and their interaction in a suspending fluid and describe
benchmark tests to validate the models for fluid-filled bodies.
