Biofilms are complex communities of microorganisms attached to surfaces or associated with interfaces. The recent explosion in biofilm research is motivated by their ubiquitous presence in environment as well as the development of new technologies such as microbial induced calcite precipitation for crack cementation, remediation for radionuclides, construction, and stabilisation of soils, and medicine. Computational models of biofilm growth and biofilm morphology are formulated at multiple scales and combine nonlinear coupled systems of reactive transport equations in evolving geometries. The main difficulty is in handling interfaces between the biofilm produced protective envelope called EPS (extracellular polymeric substance) and the bulk fluids which (may) also contain biomass. In the talk we present our new model of biofilm evolution using variational inequalities which is coupled to Navier-Stokes equations describing the bulk fluid. The model is applied at porescale where we pursue analyses and comparison with biofilm imaging (work joint with Dorthe Wildenschild and Anna Trykozko). We also extend it further to biocementation models in collaboration with OSU and DOE-NETL scientists. Furthermore, we discuss upscaling from pore to corescale. This is joint work with A. Trykozko (University of Warsaw), OSU scientists: D. Wildenschild, G. Iltis, S. Schlueter, M. Torres, I. Alleau, R. Colwell, D. Koley, A. Thurber, and DOE-NETL scientist C. Verba.