This talk will give an overview of recent results for partial differential equation models for the emergence, formation and evolution of biological transport networks. Typically, the models describe the material pressure field using a Darcy's type equation and the dynamics of the network conductance. Randomness in the porous medium material structure is represented by linear diffusion and conductance relaxation by an algebraic decay term. Micro- and mesoscopic models will be introduced and will show how they are connected to the classical macroscopic PDE system (by D. Hu and D. Cai) and to discrete graph based models.
