We report on theoretical studies of one-dimensional (1D) monatomic metal nanostructures coupled to metal substrates, which support surface states. The aim of the work is to demonstrate general features of electronic structure, magnetic properties, and interactions in such systems. We start from simple finite monatomic chains. It is shown that electronic confinement in 1D metallic chains can be observed at energies of projected band gaps of a metallic substrate. At other energies the confinement is significantly suppressed by scattering of chain states into the metallic substrate. Although this scattering decreases the exchange interaction between magnetic atoms incorporated into the chain, we show that it is still possible to get a significant enhancement of the exchange interaction in short chains. The next problem addressed in the paper is related to the interaction of the surface state with ad-chains and 1D resonators. Special attention is paid to a possible impact of confinement in 1D resonators on atomic diffusion and self-organization inside them. Finally, we illustrate the theoretical approach for the treatment of magnetization dynamics in 1D nanostructures.