The migration of a biofilm as a whole towards a nutrient source is called biofilm chemotaxis and occurs even if the individual microbes that compose the biofilm are neither chemotactic nor motile. This interesting phenomenon is caused by anisotropic growth with higher rates of cell proliferation and extracellular matrix synthesis along the nutrient concentration gradient. Fluid flow tends to suppress biofilm chemotaxis through metastatic events that involve the downstream relocation of biofilms via creep or detachment. Under certain conditions, biofilms have been experimentally observed to overcome fluid stresses and migrate against the direction of flow in porous media. This talk will mostly revolve around a computational demonstration of upstream biofilm migration that is driven by a carbon-rich nutrient supply within a granular porous medium. Such conditions are, for instance, encountered after the infiltration of crude oil in oligotrophic sediments, sand and soils where the dissolution and primary degradation of the oil generate a dispersing plume of dissolved carbon. The process is analyzed at the pore scale with a hybrid computer simulator. Specifically, the Navier-Stokes-Brinkman equations, poroelasticity equations, and convection-diffusion-reaction equations are solved numerically for the determination of the fluid velocity, biofilm stress, and solute concentration fields. Biofilm growth is described with an on-lattice cellular dynamics model and biofilm metastasis is described with a three-step (crack-roll-flow), on/off-lattice particle transport model. Mathematical, algorithmic and open issues related to the modeling approach will also be discussed.