  We briefly review recent advances in the hydrodynamic modeling of the
dynamics of droplets on adaptive substrates, in particular, solids that are
covered by polymer brushes. Thereby, the focus are long-wave and full-curvature
variants of mesoscopic hydrodynamic models in gradient dynamics form. After
introducing the approach for films/drops of nonvolatile simple liquids on rigid
smooth solid substrate, it is first expanded to an arbitrary number of coupled
degrees of freedom, before considering the specific case of drops of volatile
liquids on brush-covered solids. After presenting the model its usage is
illustrated by briefly considering the natural and forced spreading of drops of
nonvolatile liquids on a horizontal brush-covered substrate as well as drops
sliding down a brush-covered incline. Finally, also volatile liquids are
considered.
