3D graphics engines render images in video games using a combination of mathematics, geometry, and shading techniques. Initially, 3D objects are represented with polygons, which the engine processes using geometric transformations (translation, rotation, scaling). The engine then applies lighting effects, texture mapping, and shaders to create realistic appearances. It also handles camera perspectives and field of view, simulating how humans perceive depth. Additionally, optimized algorithms ensure smooth rendering framerates, enhancing the overall gaming experience for users.