Abstract : This thesis uses methods and models from non-equilibrium statistical physics to describe intracellular processes. Bidirectional microtubule-based transport within axons is modeled as a quasi-one-dimensional stochastic lattice gas with two particle species moving in opposite directions under mutual exclusion interaction. Generically occurring clusters of particles in current models for intracellular transport can be dissolved by additionally considering the dynamics of the transport lattice, i.e., the microtubule. An idealized model for the lattice dynamics is used to create a phase transition toward a homogenous state with efficient transport in both directions. In the thermodynamic limit, a steady state property of the dynamic lattice limits the maximal size of clusters. Lane formation mechanisms which are due to specific particle-particle interactions turn out to be very sensitive to the model assumptions. Furthermore, even if some particle-particle interaction is considered, taking the lattice dynamics into account almost always improves transport. Thus the lattice dynamics seems to be the key aspect in understanding how nature regulates intracellular traffic. The last part introduces a model for the dynamics of a microtubule which is limited in its growth by the cell boundary. The action of a rescue-enhancing protein which is added to the growing tip of a microtubule and then slowly dissociates leads to interesting aging effects which should be experimentally observable.