The structural behavior of mineral Stromeyerite, AgCuS, has been studied by means of angle-dispersive X-ray diffraction measurements up to 13 GPa and ab initio total-energy calculations. Two high-pressure phase transitions are found at 1.4 and 5.7 GPa, from the initial distorted Ni2In-type phase (AuRbS-type, RP, space group Cmc2(1)) through an anti-PbClF-type phase (HP1, space group P4/nmm) to a monoclinic distortion of this latter phase (HP2, space group P2(1)/m). The collapse of the metal-metal interatomic distances at the RP-HP1 transition suggests a stronger metallic behavior of the high-pressure phase. The compressibility of the lattice parameters and the equation of state of the first pressure-induced phase have been experimentally determined. First-principles calculations present an overall agreement with the experimental results in terms of the high-pressure sequence and provide chemical insight into the AgCuS behavior under hydrostatic pressure.