Epithelial tissues are composed of layers of tightly connected cells shaped into complex three-dimensional (3D) structures such as cysts, tubules, or invaginations. These complex 3D structures are important for organ-specific functions and often create biochemical gradients that guide cell positioning and compartmentalization within the organ. One of the main functions of epithelia is to act as physical barriers that protect the underlying tissues from external insults. In vitro, epithelial barriers are usually mimicked by oversimplified models based on cell lines grown as monolayers on flat surfaces. While useful to answer certain questions, these models cannot fully capture the in vivo organ physiology and often yield poor predictions. In order to progress further in basic and translational research, disease modeling, drug discovery, and regenerative medicine, it is essential to advance the development of new in vitro predictive models of epithelial tissues that are capable of representing the in vivo-like structures and organ functionality more accurately. Here, we review current strategies for obtaining biomimetic systems in the form of advanced in vitro models that allow for more reliable and safer preclinical tests. The current state of the art and potential applications of self-organized cell-based systems, organ-on-a-chip devices that incorporate sensors and monitoring capabilities, as well as microfabrication techniques including bioprinting and photolithography, are discussed. These techniques could be combined to help provide highly predictive drug tests for patient-specific conditions in the near future.