  Three problems in the statistical mechanics of models for an assembly of
molecular motors interacting with cytoskeletal filaments are reviewed. First, a
description of the hydrodynamical behaviour of density-density correlations in
fluctuating ratchet models for interacting molecular motors is outlined.
Numerical evidence indicates that the scaling properties of dynamical behavior
in such models belong to the KPZ universality class. Second, the generalization
of such models to include boundary injection and removal of motors is provided.
In common with known results for the asymmetric exclusion processes,
simulations indicate that such models exhibit sharp boundary driven phase
transitions in the thermodynamic limit. In the third part of this paper, recent
progress towards a continuum description of pattern formation in mixtures of
motors and microtubules is described, and a non-equilibrium ``phase-diagram''
for such systems discussed.
