The discovery of biofilm formation in bacteria and yeasts has led to a better understanding of microbial ecology and to new insights into the mechanisms of virulence and persistence of pathogenic microorganisms. However, it is generally assumed that filamentous fungi, some of which have a significant impact on our health or our economy, do not form biofilms. In contrast to this assumption, here we discuss recent findings supporting the hypothesis that surface-associated filamentous fungi can form biofilms. Based on these findings and on previous models for bacterial and yeast systems, we propose preliminary criteria and a model for biofilm formation by filamentous fungi.