The important and diverse roles of the gut microbiota in human health and disease are increasingly recognized. The difficulty of inferring causation from metagenomic microbiome sequencing studies and from mouse-human interspecies differences has prompted the development of sophisticated in vitro models of human gut-microbe interactions. Here, we review recent advances in the co-culture of microbes with intestinal and colonic epithelia, comparing the rapidly developing fields of organoids and organs-on-chips with other standard models. We describe how specific individual processes by which microbes and epithelia interact can be recapitulated in vitro. Using examples of bacterial, viral, and parasitic infections, we highlight the advantages of each culture model and discuss current trends and future possibilities to build more complex co-cultures.