  Using minimal models for low Reynolds number passive and active rotors in a
fluid, we characterize the hydrodynamic interactions among rotors and the
resulting dynamics of a pair of interacting rotors. This allows us to treat in
a common framework passive or externally driven rotors, such as magnetic
colloids driven by a rotating magnetic field, and active or internally driven
rotors, such as sperm cells confined at boundaries. The hydrodynamic
interaction of passive rotors is known to contain an azimuthal component \sim
1/r^2 to dipolar order that can yield the recently discovered "cooperative
self-propulsion" of a pair of rotors of opposite vorticity. While this
interaction is identically zero for active rotors as a consequence of torque
balance, we show that a \sim 1/r^4 azimuthal component of the interaction
arises in active systems to octupolar order. Cooperative self-propulsion,
although weaker, can therefore also occur for pairs of active rotors.
