The structure and dynamics of networks formed by rod-shaped particles can be indirectly investigated by measuring the diffusion of spherical tracer particles. This method was used to characterize cellulose nanofibril (CNF) networks in both dispersed and arrested states, the results of which were compared with coarse-grained Brownian dynamics simulations. At a CNF concentration of 0.2 wt% a transition was observed where, below this concentration tracer diffusion is governed by the increasing macroscopic viscosity of the dispersion. Above 0.2 wt%, the diffusion of small particles (20-40 nm) remains viscosity controlled, while particles (100-500 nm) become trapped in the CNF network. Sedimentation of silica microparticles (1-5 mu m) in CNF dispersions was also determined, showing that sedimentation of larger particles is significantly affected by the presence of CNF. At concentrations of 0.2 wt%, the sedimentation velocity of 5 mu m particles was reduced by 99 % compared to pure water.