Metal nanoparticles supported on solid surfaces constitute the active component of many catalysts used in energy conversion, electrocatalysis, and environmental applications. Their catalytic performance is governed not only by particle size and composition but also by the electronic interaction with the supporting material, which determines nanoparticle stability, strain, and surface reactivity. This presentation summarizes a series of density functional theory (DFT) investigations aimed at revealing the atomic-scale mechanisms governing the electronic properties and stability of supported nanoparticles across carbon, oxide, and mixed metal-oxide supports. Systematic DFT calculations demonstrate that the binding strength of Pd and Au nanoparticles can be tuned through the surface curvature. Highly curved surfaces induce stronger orbital overlap, significantly increasing adsorption energies and suppressing nanoparticle mobility. First-principles molecular dynamics simulations further reveal reduced nanoparticle migration on curved supports, providing a microscopic explanation for the experimentally observed enhancement in catalyst durability. Platinum nanoparticles supported on carbon and SnO₂ demonstrate that strong metal-support interactions with oxide surfaces induce pronounced lattice distortions extending throughout the nanoparticle. Atomic-scale defects on the oxide support generate localized strain fields that modify the Pt electronic structure, providing an atomistic explanation for the experimentally measured strain distributions and their correlation with catalytic activity. Finally, we addresses self-exsolved Cu/Fe₃O₄ heterostructured nanoparticles formed during CO₂/H₂O co-electrolysis on CuFe₂O₄ spinel electrodes. First-principles calculations reveal that the metal-oxide interface creates electronically distinct active sites unavailable on the individual phases. Charge redistribution across the Cu/Fe₃O₄ interface promotes activation of CO₂ and H₂O while simultaneously stabilizing the exsolved nanoparticles through strong interfacial bonding. The calculations explain the exceptional activity and long-term stability observed experimentally and identify the heterostructured cermet interface as the primary catalytic active site.Together, these studies demonstrate how first-principles simulations can establish direct relationships between support geometry, electronic structure, lattice strain, and nanoparticle stability. By combining electronic structure theory with advanced experimental characterization, they provide fundamental design principles for engineering robust nanocatalysts with enhanced activity and durability for electrochemical energy conversion and heterogeneous catalysis.