Copper (Cu) can be considered as a biological yin-yang element, because it is essential but toxic at the same time. To manage this paradox, cells have evolved complex molecular Cu transport pathways, in which Cu chaperones bind and shuttle Cu to specific intracellular targets. In humans, Atox1 delivers Cu(I) to the metal-binding domains (MBDs) of Cu-ATPases, the Menkes and Wilson disease proteins, for subsequent incorporation into cuproenzymes. Both metallochaperones and target MBDs adopt the same ferredoxin-like fold and bind Cu(I) via two Cys residues in a conserved motif. In this thesis, we have employed a wide selection of state-of-the-art computational schemes, including quantum mechanics and molecular mechanics methodologies in combination with molecular dynamics simulations, to broaden our understanding on the structure-function relationships of Cu chaperones, MBDs, and their interactions. This work reports on a thorough study of the structural dynamics, Cu-binding properties, protein-protein interactions and Cu-transfer mechanisms of key Cu transport proteins, and how conserved residues modulate these properties. We found that residues framing the Cu loop have evolved differently in prokaryotic and eukaryotic Cu chaperones to tune the flexibility and provide an optimal stabilization of the Cu loop. Some of these residues are also key for metallochaperone-MBD interactions and subsequent Cu(I) transfer. We further found that the MBDs are not equivalent at the molecular level, and propose that backbone flexibility together with electrostatic complementarity are important factors to guide Atox1 interactions. We propose that Atox1 interacts with its partner MBDs via a "weak" interface that can be disrupted by at least one substitution in Atox1. Finally, we have elucidated for the first time the Cu(I) transfer mechanism from holo-Atox1 to an apo-MBD, and propose that the reaction proceeds with the existence of two trigonal intermediates. Our results suggest that the reaction is kinetically feasible but not energetically favorable, pointing to the apparent absence of a thermodynamic gradient for Cu(I) transfer. The structural, dynamic, thermodynamic and mechanistic details obtained here with atomic resolution are difficult to obtain by in vitro experiments, and can be used both as a complement to experiments and as predictive tools for functional insights.