Copper plays a vital role in fundamental cellular functions, and its concentration in the cell must be tightly regulated, as dysfunction of copper homeostasis is linked to severe neurological diseases and cancer. This review provides a compendium of current knowledge regarding the mechanism of copper transfer from the blood system to the Golgi apparatus; this mechanism involves the copper transporter hCtr1, the metallochaperone Atox1, and the ATPases ATP7A/B. We discuss key insights regarding the structural and functional properties of the hCtr1-Atox1-ATP7B cycle, obtained from diverse studies relying on distinct yet complementary biophysical, biochemical, and computational methods. We further address the mechanistic aspects of the cycle that continue to remain elusive. These knowledge gaps must be filled in order to be able to harness our understanding of copper transfer to develop therapeutic approaches with the capacity to modulate copper metabolism.