Replicating the in vitro properties of tissue barriers—such as the blood-brain barrier, gut, skin, lung, kidney, retina, nasal epithelium, and placenta—is crucial for many applications, including drug screening, studying molecular transport, drug delivery, and disease modeling in preclinical studies. Organ-on-a-chip (OoC) platforms are advanced three-dimensional (3D) in vitro models that aim to replicate various aspects of organ functionality within microfluidic systems by providing microenvironments akin to native tissue. When used to model the interface between two different tissue compartments, OoC technology offers a promising platform for more accurately replicating the physiology and pathophysiology of various tissue barriers in the body. This review focuses on the state-of-the-art biomimetic tissue barrier models, ranging from two-channel tissue barrier-on-a-chip systems with a thin porous membrane to hydrogel-based membrane models. Specifically, it explores the engineering of tissue barrier-on-a-chip platforms, highlighting various fabrication techniques for microfluidic chips and membranes, as well as methods for functional characterization of the engineered tissue barriers. Additionally, we discuss the development of organ-specific barrier models and multi-organ-on-a-chip systems for studying inter-organ communication. Finally, we highlight the current challenges in the field and future directions in advancing tissue barrier modeling using OoC technology.