  Because active particles break time-reversal symmetry, a single non-spherical
body placed in an active fluid generates currents. We show that when two or
more passive bodies are placed in an active fluid these currents lead to
long-range interactions. Using a multipole expansion we characterize their
leading-order behaviors in terms of single-body properties and show that they
decay as a power law with the distance between the bodies, are anisotropic, and
do not obey an action--reaction principle. The interactions lead to rich
dynamics of the bodies, illustrated by the spontaneous synchronized rotation of
pinned non-chiral bodies and the formation of traveling bound pairs. The
occurrence of these phenomena depends on tunable properties of the bodies, thus
opening new possibilities for self-assembly mediated by active fluids.
