Many mathematical models have been created in an effort to improve our understanding of biofilters, to guide experimentation, and to improve design of biological treatment systems. The approaches used to model gas flow, phase transfer, diffusion within the biofilm, and biological growth have become relatively standard. Further progress on these phenomena will come primarily from improved determinations of important model parameters under various conditions. There is less unanimity and less certainty in the approaches that have been taken to account for biofilm growth, the complex conformation of the biofilm takes within the porous packing, and the details of the processes by which biofilters become clogged. Biofilter and biotrickling filter models have been useful for research purposes, but have not yet progressed to the point of being reliable and generally accepted tools for design. (c) 2005 Elsevier B.V. All rights reserved.