Using the fully relativistic version of the Korringa-Kohn-Rostoker method for electronic structure calculations within local spin density functional theory, the magnetic and spectroscopic properties of Co clusters deposited on Pt(111) have been investigated. Of central interest was the role of spin orbit coupling, since it influences the spontaneous formation and orientation of magnetic moments and gives rise among other things to the occurrence of orbital magnetic moments, magnetic anisotropy energy and magnetic circular dichroism in X-ray absorption. The results have been complemented by calculations of the exchange coupling parameters J(ij) used within Monte Carlo simulations on the basis of the extended classical Heisenberg Hamiltonian. This allowed us to simulate the magnetic properties at finite temperatures, which are of central importance for applications.