The intestinal epithelium has one of the highest turnover rates in the human body, which is supported by intestinal stem cells. Culture models of intestinal physiology have been evolving to incorporate different tissue and microenvironmental elements. However, these models also display gaps that limit their similarity with native conditions. Microfluidics technology arose from the application of microfabrication techniques to fluid manipulation. Recently, microfluidic approaches have been coupled with cell culture, creating self-contained and modular in vitro models with easily controllable features named organs-on-chip. Intestine-on-chip models have enabled the recreation of the proliferative and differentiated compartments of the intestinal epithelium, the long-term maintenance of commensals, and the intraluminal perfusion of organoids. In addition, studies based on human primary intestinal cells have shown that these systems have a closer transcriptomic profile and functionality to the intestine in vivo, when compared with other in vitro models. The design flexibility inherent to microfluidic technology allows the simultaneous combination of components such as shear stress, peristalsis-like strain, 3-dimensional structure, oxygen gradient, and co-cultures with other important cell types involved in gut physiology. The versatility and complexity of the intestine-on-chip grants it the potential for applications in disease modeling, host-microbiota studies, stem cell biology, and, ultimately, the translation to the pharmaceutical industry and clinics as a reliable high-throughput platform for drug testing and personalized medicine, respectively. This review focuses on the physiological importance of several components that have been incorporated into intestine-on-chip models and highlights interesting features developed in other types of in vitro models that might contribute to the refinement of these systems.