A smiley face rendered in SVG uses React to structure its elements and D3's `arc` generator to draw the mouth. The face consists of a red circular head with a black stroke, two fixed-position eyes, and a curved mouth path created with inner and outer radii. The code defines constant dimensions for the face, eyes, and mouth, then applies a translation transform to center everything. React DOM renders the SVG tree, while D3 v5 handles the arc path calculation, demonstrating a straightforward integration of the two libraries.