The fluid flow, species transport, and chemical reactions in geological formations are the chief mechanisms in engineering the exploitation of fossil fuels and geothermal energy, the geological storage of carbon dioxide (CO), and the disposal of hazardous materials. Porous rock is characterized by a wide surface area, where the physicochemical fluid-solid interactions dominate the multiphase flow behavior. A variety of visual models with differences in dimensions, patterns, surface properties, and fabrication techniques have been widely utilized to simulate and directly visualize such interactions in porous media. This review discusses the six categories of visual models used in geological flow applications, including packed beds, Hele-Shaw cells, synthesized microchips (also known as microfluidic chips or micromodels), geomaterial-dominated microchips, three-dimensional (3D) microchips, and nanofluidics. For each category, critical technical points (such as surface chemistry and geometry) and practical applications are summarized. Finally, we discuss opportunities and provide a framework for the development of custom-built visual models.