The compositional and structural diversity of bimetallic nanocrystals (NCs) provides a superior tunability of their physico-chemical properties, making them attractive for a variety of applications, including sensing and catalysis. Nevertheless, the manipulation of the properties-determining features of bimetallic NCs still remains a challenge, especially when moving away from noble metals. In this work, we explore the galvanic replacement reaction (GRR) of In NCs and a copper molecular precursor to obtain Cu-In bimetallic NCs with an unprecedented variety of morphologies and distribution of the two metals. We obtain spherical Cu11In9 intermetallic and patchy phase-segregated Cu-In NCs, as well as dimer-like Cu-Cu11In9 and Cu-In NCs. In particular, we find that segregation of the two metals occurs as the GRR progresses with time or with a higher copper precursor concentration. We discover size-dependent reaction kinetics, with the smaller In NCs undergoing a slower transition across the different Cu-In configurations. We compare the obtained results with the bulk Cu In phase diagram and, interestingly, find that the bigger In NCs stabilize the bulk-like Cu-Cu11In9 configuration before their complete segregation into Cu-In NCs. Finally, we also prove the utility of the new family of Cu-In NCs as model catalysts to elucidate the impact of the metal elemental distribution on the selectivity of these bimetallics toward the electrochemical CO2 reduction reaction. Generally, we demonstrate that the GRR is a powerful synthetic approach beyond noble metal-containing bimetallic structures, yet that the current knowledge on this reaction is challenged when oxophilic and poorly miscible metal pairs are used.