The main focus of the thesis is to have better understanding of the atomic and electronic structures, vibrational dynamics and thermodynamics of metallic surfaces and bi-metallic nanoparticles (NPs) via a multi-scale simulational approach. The research presented here involves the study of the physical and chemical properties of metallic surfaces and NPs that are useful to determine their functionality in building novel materials. The study follows the 'bottom-up' approach for which the knowledge gathered at the scale of atoms and NPs serves as a base to build, at the macroscopic scale, materials with desired physical and chemical properties. We use a variety of theoretical and computational tools with different degrees of accuracy to study problems in different time and length scales. Interactions between the atoms are derived using both Density Functional Theory (DFT) and Embedded Atom Method (EAM), depending on the scale of the problem at hand. For some cases, both methods are used for the purpose of comparison. For revealing the local contributions to the vibrational dynamics and thermodynamics for the systems possessing site-specific environments, a local approach in real-space is used, namely Real Space Green's Function method (RSGF). For simulating diffusion of atoms/clusters and growth on metal surfaces, Molecular Statics (MS) and Molecular Dynamics (MD) methods are employed.