Living things keep themselves out of equilibrium by consuming energy from their surroundings in the form of nutrients or radiation. This allows them to move. On cellular scales, motion is driven by a dynamic network of polymer filaments (actin, microtubules) and crosslinking proteins, many of which act as molecular scale motors. Collectively this system of filaments, passive crosslinks and motors, is called the cytoskeleton. The large scale properties of this living material are shaped by the specifics of molecular scale interactions between cytoskeletal filaments. We seek to understand the forces and torques that filaments exchange. For this we need to understand the collective dynamics of crosslinking proteins that link cytoskeletal filaments. We tackle this problem by developing a theory that uses the fundamental physical principles of mass, number and momentum conservation and the symmetries of the system to derive generic equations of motion for crosslinks coupling two cytoskeltal f ilaments. In this way we can fully characterize crosslink effects between filaments, in a theory that is agnostic to microscale details.