  Recent theoretical works exploring the hydrodynamics of soft material in
non-equilibrium situations are reviewed. We discuss the role of hydrodynamic
interactions for three different systems: i) the deformation and orientation of
sedimenting semiflexible polymers, ii) the propulsion and force-rectification
with a nano-machine realized by a rotating elastic rod, and iii) the
deformation of a brush made of grafted semiflexible polymers in shear flows. In
all these examples deformable polymers are subject to various hydrodynamic
flows and hydrodynamic interactions. Perfect stiff nano-cylinders are known to
show no orientational effects as they sediment through a viscous fluid, but it
is the coupling between elasticity and hydrodynamic torques that leads to an
orientation perpendicular to the direction of sedimentation. Likewise, a
rotating stiff rod does not lead to a net propulsion in the Stokes limit, but
if bending is allowed an effective thrust develops whose strength and direction
is independent of the sense of rotation and thus acts as a rectification
device. Lastly, surface-anchored polymers are deformed by shear flows, which
modifies the effective hydrodynamic boundary condition in a non-linear fashion.
All these results are obtained with hydrodynamic Brownian dynamics simulation
techniques, as appropriate for dilute systems. Scaling analyses are presented
when possible. The common theme is the interaction between elasticity of soft
matter and hydrodynamics, which can lead to qualitatively new effects.
