The K–Au–Ga system has been investigated at 350 °C for <50 at. % K. The potassium gold gallides K0.55Au2Ga2, KAu3Ga2, KAu2Ga4 and the solid solution KAuxGa3–x (x = 0–0.33) were synthesized directly from the elements via typical high-temperature reactions, and their crystal structures were determined by single crystal X-ray diffraction: K0.55Au2Ga2 (I, I4/mcm, a = 8.860(3) Å, c = 4.834(2) Å, Z = 4), KAu3Ga2 (II, Cmcm, a = 11.078(2) Å, b = 8.486(2) Å, c = 5.569(1) Å, Z = 4), KAu2Ga4 (III, Immm, a = 4.4070(9) Å, b = 7.339(1) Å, c = 8.664(2) Å, Z = 2), KAu0.33Ga2.67 (IV, I-4m2, a = 6.0900(9) Å, c = 15.450(3) Å, Z = 6). The first two compounds contain different kinds of tunnels built of puckered six- (II) or eight-membered (I) ordered Au/Ga rings with completely different cation placements: uniaxial in I and III but in novel 2D-zigzag chains in II. III contains only infinite chains of a potassium-centered 20-vertex polyhedron (K@Au8Ga12) built of ordered 6–8–6 planar Au/Ga rings. The main structural feature of IV is dodecahedral (Au/Ga)8 clusters. Tight-binding electronic structure calculations by linear muffin-tin-orbital methods were performed for idealized models of I, II, and III to gain insights into their structure–bonding relationships. Density of states curves reveal metallic character for all compounds, and the overall crystal orbital Hamilton populations are dominated by polar covalent Au–Ga bonds. The relativistic effects of gold lead to formation of bonds of greater population with most post-transition elements or to itself, and these appear to be responsible for a variety of compounds, as in the K–Au–Ga system.