  A particle placed in soft matter distorts its host and creates an energy
landscape. This can occur, for example, for particles in liquid crystals, for
particles on lipid bilayers or for particles trapped at fluid interfaces. Such
energies can be used to direct particles to assemble with remarkable degrees of
control over orientation and structure. These notes explore that concept for
capillary interactions, beginning with particle trapping at fluid interfaces,
addressing pair interactions on planar interfaces and culminating with
curvature capillary migration. Particular care is given to the solution of the
associated boundary value problems to determine the energies of interaction.
Experimental exploration of these interactions on planar and curved interfaces
is described. Theory and experiment are compared. These interactions provide a
rich toolkit for directed assembly of materials, and, owing to their close
analogy to related systems, pave the way to new explorations in materials
science.
