Neutral bis(amino acidato)copper(II) [Cu(aa)2] coordination compounds are the physiological species of copper(II) amino acid compounds in blood plasma taking the form of bis(l-histidinato)copper(II) and mixed ternary copper(II)-l-histidine complexes, preferably with l-glutamine, l-threonine, l-asparagine, and l-cysteine. These amino acids have three functional groups that can bind metal ions: the common α-amino and carboxylate groups and a side-chain polar group. In Cu(aa)2, two coordinating groups per amino acid bind to copper(II) in-plane, while the third group can bind apically, which yields many possibilities for axial and planar bonds, that is, for bidentate and tridentate binding. So far, the experimental studies of physiological Cu(aa)2 compounds in solutions have not specified their complete geometries. This paper provides a brief review of my group's research on structural properties of physiological Cu(aa)2 calculated using the density functional theory (DFT) to locate low-energy conformers that can coexist in aqueous solutions. These DFT investigations have revealed high conformational flexibility of ternary Cu(aa)2 compounds for tridentate or bidentate chelation, which may explain copper(II) exchange reactions in the plasma and inform the development of small multifunctional copper(II)-binding drugs with several possible copper(II)-binding groups. Furthermore, our prediction of metal ion affinities for Cu2+ binding with amino-acid ligands in low-energy conformers with different coordination modes of five physiological Cu(aa)2 in aqueous solution supports the findings of their abundance in human plasma obtained with chemical speciation modelling.