Summary. R. developed a simple chemostat-based model of competition between two bacterial strains, one of which is capable of wall-growth, in order to illuminate the role of bacterial wall attachment on the phenomenon of colonization resistance in the mammalian gut. Together with various collaborators, we have re-formulated the model in the setting of a tubular flow reactor, extended the interpretation of the model as a biofilm model, and provided both mathematical analysis and numerical simulations of solution behavior. The present paper provides a review of the work in [5,6,4,52,50,36,33,32,35,34].Introduction. The ability of bacteria to colonize surfaces forming biofilms and thereby to create a refuge from the vagaries of fluid advection has stimulated a great deal of recent research in a variety of disciplines. The importance of wall growth was first made apparent to us from the work of microbiologist Rolf Freter and his colleagues [25,27,26,24]. Their mathematical models of the phenomenon of colonization resistance in the mammalian gut showed that bacterial wall attachment could play a crucial role in the observed stability of the natural microflora of the gut to invasion by non-indigenous microorganisms. The authors had the pleasure of learning of this work first hand from a lecture by Freter at the Microbial Ecology Workshop organized by Frank Hoppensteadt and Smith at Arizona State University in 1997. Our own work can be traced to a collaboration that began at this workshop.While Freter's model was formulated in a CSTR (chemostat) setting which is natural since this reactor mimics the mouse cecum, the animal model for gut research, we felt that another natural setting was the plug flow reactor (PFR) where bacterial motility, fluid advection, and other spatial effects could play a larger role. The flow reactor more accurately reflects the environment of the large intestine of humans. Thus, Ballyk and Smith formulated a family of models for microbial growth and competition for limiting substrate and wall-attachment sites in our first work [5]. This paper focused on describing the model equations which consist of a system of parabolic partial differential